User:DroneBetter/qfind results

From LifeWiki
< User:DroneBetter
Revision as of 16:48, 27 April 2024 by Prime Raptor21 (talk | contribs) (→‎B36/S12 ({{rl|HighFlock}}): Min width symmetric trivially exists by having two copies of the min width asymmetric ship...looking for more interesting examples though.)
Jump to navigation Jump to search

I had long assumed that openmp was simply not yet supported on macOS until I learned that the gcc command in fact uses Clang albeit named misleadingly

as such, having used Homebrew, I am now able to compile qfind, and finally create tables of bounds upon spaceship widths (which I will do here :-)

all links included are to the minimal spaceship found (first outputted, only minimal by bounding box, not population), however (where a table cell is split) the second subrow excludes members of a subset of the symmetry and those comprised of two smaller noninteracting spaceships, choosing the first nontrivial output instead to maximise information content

note that alike its gfind ancestor of yore, qfind is restricted to orthogonal searches, however it is very fast at them

you may add your own results (disproofs for lower bounds and spaceship examples for upper), however I think (to avoid confusion) I would like others to include citations of forum posts in which they explicitly state their results, so that those uncited can be attributed to me by default without having to go through the page's history

no gutter column is included for rules that are not gutter-preserving

thank you very dearly to ascendantDreamweaver for using a 48-core computer with 512GB of RAM to which they had access, for increasing logical widths for 2c/5 and 3c/7 to 12 in the first four rules (except for B36/S12, in which 2c/5's are small enough that I managed on my own)

all results labelled as JLS are due to wwei23

B36/S245 (sqrt replicator rule)

(I like the name a lot for some reason)

ascendantDreamweaver did the searches that led to finding the asymmetrical 2c/5 and 2c/7, as well as obtaining the present best lower bounds for 3c/7, 3c/8 (except for the 3c/8 even, which they found), 4c/9 and 5c/11

Velocity Asymmetric Odd-symmetric Even-symmetric
(1,0)c/2 6 13 14
(1,0)c/3 6 11[n 1] 6
6
(1,0)c/4 4 9 10
12
(2,0)c/4 7 13 14
(1,0)c/5 8 11 12
(2,0)c/5 12 19 20
(1,0)c/6 9 13 14
(2,0)c/6 7 11 10
(3,0)c/6 7 13 14
(1,0)c/7 9[n 2] 13 14
(2,0)c/7 11[n 3] 17[n 4] 16
(3,0)c/7 12 23 24
(1,0)c/8 6 11 12
(2,0)c/8 7 9 12
(3,0)c/8 10[n 5] 19[n 6] 20
(4,0)c/8 7 13 14
(1,0)c/9 5 9 10
(2,0)c/9 6 11 12
(3,0)c/9 7 11 12
(4,0)c/9 10 19[n 7] 20[n 8]
(1,0)c/10 5 9 10
(2,0)c/10 6 11 12
(3,0)c/10 7 13 14
(4,0)c/10 8 15 16
(5,0)c/10 7 13 14
(1,0)c/11 5 9 10
(2,0)c/11 6 11 12[n 9]
(3,0)c/11 7 11 12
(4,0)c/11 8 15 14[n 10]
(5,0)c/11 10 19[n 11] 20[n 12]
(1,0)c/12 5 9 10
(2,0)c/12 5 9 10
(3,0)c/12 5 9 10
(4,0)c/12 6 9 10
(5,0)c/12 7 13 14
(6,0)c/12 7 13 14
(4,0)c/14 5 9 12
(7,0)c/14 6 11 12
(10,0)c/20 5 < w ≤ 10 9 10
(4,0)c/23 3 5 6 < w ≤ 10
(26,0)c/52 w ≤ 17

I found the 4c/14 with ikpx2 as a new speed before performing qfind searches up to width 10 that proved its minimality, then found the true-period 2c/7's

I also found a (1,1)c/5, (2,1)c/5 and (1,1)c/6 with ikpx2, each the first of its velocity as well, also shown in this table in spite of nonminimal width

x = 839, y = 265, rule = B36/S245 b2o3b4o3b4o4b4o5b4o4b4o5b4o6b4o8b4o12b4o9b4o2b4o5b4o2b4o9b4o9b4o2b4o6b4ob4o6b4ob4o4b4o5b4o2b4o5b4o4b4ob4o4b4o5b4o3b4o3b4o8b6o4b4o9b4o10b4o18b4o11b4o4b4o6b4o4b5ob5o3b4o5b4o5b5ob5o3b4o7b4o6b5ob5o2b7o8b9o10b4o10b4o6b4o4b3o8b4o8b3o6b3o8b4o8b4o5b3ob3o9b2o12b2o10b4o6b4o9b3o11b2o12b5o12b2o24bob5o7b3o38b2o17b3o14b2o11bobo14bo$4o3b2o5b2o6b2o7b2o6b2o7b2o8b2o7bobo2bobo8bobo2bobo8b2o4b2o7b2o4b2o8bobo2bobo8b2o4b2o8b2o3b2o8b2o3b2o6b2o7b2o4b2o7b2o6b2o3b2o6b2o7b2o5b2o5b2o8bo3b2o5bo2bo4bo4bo2bo3b5o3b2o3b5o12b2o11b6o2b6o4b6o4b3o3b3o3b6o3b6o5b3o3b3o3b6o5b6o6b3o3b3o4b2ob2o9bobobobobo8bobo2bobo6bo2b2o2bo4b4o2b7o7b2o8bo3bo3b7o6b4o9b2o5b2obobob2o7b4o10b4o10b2o7b2obo5b11o5b6o8b2o2bo2b2o9bo2bo22bob3ob3o6bob2o36b4o19b2o13b2o11b3o13b2o$bo2bobobo3b2obo4b2obo5b2obo4b2obo5b2obo6b2obo6b4o2b4o6b4o2b4o5b2ob6ob2o3b2ob6ob2o5b4o2b4o5b2obo4bob2o4b2obo3bob2o4b2obo3bob2o4bob2o3b2obo4bob2o3b2obo4b2obo3bob2o4bob2o3b2obo3b2obo5bob2o12b2o3bo3bobobobobo3bo6bo2b6o2bo7b6obo2bob6o3bo4bo2bo4bo4bo4bo4bo2bobo2bo3bo4bo3bo4bo5bo2bobo2bo3bo4bo5bo4bo6bo2bobo2bo5b2ob2o7b5ob5o9b4o9bo4bo6b2o4bobobo6bo4bo6bo3bo4b5o8b2o9b2obo3b5ob5o5bob2obo8bob2obo19b2o7b2o5b2o6bo4bo9bo5bo34b2o5b2ob2o5bo2bo38b2o18b2o11bobobo11b2obo12b3o$bo9b2o6b2o7b2o6b2o7b2o8b2o8bobo2b2o2bobo4bobo2b2o2bobo3b2o3bo2bo3b2ob2o3bo2bo3b2o3bobo2b2o2bobo3b2o10b2o2b2o9b2o2b2o9b2o6b2ob2o10b2ob2o6b2o9b2o6b2ob2o5b2o11b2o5b2obob2o4bo5bobobo5bo4bob2o3b2o3b2obo7b3o8b3o7b2o6b2o8b2o7bobobobo6b2o7b2o8bobobobo6b2o9b2o9bobobobo5b4obo6bobob5obobo8bo2bo9b6o12b5o6b6o6b2ob2o4bobobo18b2ob3o3b3o3b3o6bob2obo8bob2obo6b2o4b2o5bo2bo5bobo3bobo21b3ob3o7bo2b4o2bo16bo4bo2b2ob2o7b3o33bob2o2b2o13bob4o10b2ob2o11b3o$12bo6bob2o5bob2o5bo7bob2o7bo7bo4b4o4bo2bo4b4o4bo5bo6bo7bo6bo5bo4b4o4bo3bo10bo4bo9bo4bo9bo7bo3bo10bo3bo7bo9bo7bo3bo6bo11bo9bo2bo12bo14b2ob2o2b2ob2o7bob2o10b2obo4b4o4b4o6b4o7bo3bo6b4o5b4o8bo3bo6b4o7b4o9bo3bo6bob2o9b3ob3ob3o8b2o2b2o8bo4bo7bo4b2ob2o6bo4bo8bo5b2o3b2o6bo2bo7b3o6b3o3b3o7b4o10b4o7b2o4b2o3bo3b2o5bobo3bobo5b2o4b2o8bobobobo6b2o2b4o2b2o18b3o3b2obo7bo36b2o3b3o11bob2o2b2o10bo2b2o6b2ob2o2bo$11bo2bo5b3obo4b3obo2bo2bo6b3obo4bo2bo6bob8obo4bob8obo7bob2obo9bob2obo7bob8obo3bo2bob4obo2bo2bo2bo5bo2bo2bo2bo5bo2bo4bo2bobo2bo6bo2bobo2bo4bo2bo5bo2bo4bo2bobo2bo3bo2bo7bo2bo7b3o12bo3bo11b2o10b2o28b4o4b4o5bob2obo7b3o7b4o5b4o9b3o7b4o7b4o10b3o6bobo3bo5b7ob7o4b3ob2ob3o4bobo4bobo4b2o3bo2bo2bo4b3o2b3o14bo3bo8b2o9b2ob2o2b2o7b2o31bo6bo4bobob2o3bob2o3b2obo4bo2b2o2bo9bo3bo8b3o4b3o17bob3o3b3o7bobo33b4o2bob2o12b2obo11b3obo8bo5bo$12bo2b2o3bo3b2o3bo3b2o2bo2b2o4bo3b2o4bo2b2o3bobob2o2b2obobo2bobob2o2b2obobo6bob2obo9bob2obo6bobob2o2b2obobo3bo3bo2bo3bo4bo2b2ob2o2bo4bo2b2ob2o2bo3b2o2bo3bo2b2o2b2o2bo3bo2b2o3bo2b2ob2o2bo3b2o2bo3bo2b2o2bo2b2o3b2o2bo8b3ob2o9bo3bo34bo10bo6bob2obo2bob2obo4b6o7b3o6bob2obo4bo2bo9b3o6bob2obo5b6o9b3o8b4o7bo11bo5b2o6b2o3b3obo2bob3o4b2o11b3obo2bob3o4bobo4b2o3b2o5bob2obo6bob3o3bobo5bobo4bo2b2o2bo6bo2b2o2bo17bob3obo17bo6bo10bobo7bo2b2o4b2o2bo13b2o2b2o2b2o9b4o32bo4b3obo8b3ob2obo9bo3b3o7b2obobo$14b2o3bo2b3o3bo2b3o5b2o4bo2b3o7b2o6b2obo2bob2o6b2obo2bob2o6bo8bo5bo8bo6b2obo2bob2o4b2o10b2o5b2o3b2o8b2o3b2o6b2o7b2o4b2o7b2o6b2o3b2o6b2o7b2o5b2o5b2o10b3o12bobobo12bo3b4o3bo9bo2bo6bo2bo5bob2obo2bob2obo4bo4bo6bobobo5bob2obo4b4o8bobobo5bob2obo4b2o4b2o7bobobo6bobob2o8bo7bo8b2ob2ob2o4bo2bob2obo2bo9b5o4b2o6b2o6bo4b2o5b2o2b2obo2bob2o3bobo7b2o5b2o5b8o6b8o20bob3o16b2o4b2o10bobo7b2o10b2o14b2o2b3o2bo7b2obo27bo5bo4b2o9bobo2b2o12b4ob3o7bo3bo$13b3o8b2o7b2o2bob2obo7b2o4bob2obo3b3o6b3o4b3o6b3o7bo4bo9bo4bo9b2o4b2o7bo8bo6b3o3b3o9bobo8b3o5b3o4b3o5b3o5b3o3b3o5b3o5b3o3bob2obobob2obo8bob5o7bobobobo10bobobob2obobobo8bobo8bobo23b2o2b2o6b2ob2o16b2o9b2ob2o16b2o2b2o8b2ob2o8b3o10b2o3b2o11b4o7bobo4bobo12bo6bobob2obobo4b2ob2o4bo3bo4b2obo2bob2o4b2obo5b2o5b2o4b2ob4ob2o4b2ob4ob2o19bo3bo35bo11b2o4b2o16bobo2b4o8b5o28b4obo4bobo8bo5bo13b4o10b4o$14bo8b2o7b2o3b6o6b2o5b6o3b3o6b3o3bob2o6b2obo23b2o10bo8bo6bo8bo6b3o3b3o6bo7bo6bo7bo6bo7bo7bo5bo7bo7bo4b6ob6o6b3o2bob2o6b4ob4o9bo4bo2bo4bo9b2o8b2o7bo2bo4bo2bo3b2o6b2o15bo2bo3b2o4b2o17bo2bo6bo4bo22bobo6b2o2b2ob2o2b2o41bo5b2o3b2o3b2o12bo3bo5b2ob2ob2o6bo20bobo4bobo4bobo4bobo19bo2bo17b2o4b2o10bobo9b3o4b3o18bobob3o5b4o2bo27bo2bo7bo8b2o2b3ob2o9bob2o3bo5b2o3bo2bo$11b2ob3o6b3o6b3o3bo2bo7b3o5bo2bo3bob2o6b2obo2bob2o6b2obo22b4o9b2o6b2o6b3o4b3o5b2obobobob2o6bobobobo5b3ob2ob2ob3o2b3ob2ob2ob3o2b2ob3ob3ob2o2b3ob2ob2ob3o3bo2bo3bo2bo6b3o3bo3bo2bob2o2bobo2b2obo5bo4bo4bo4bo42b4o2b4o3bobobobo12b3o2b3o5bobobobo14bobo2bobo6bobobobo9bobo5bobob2ob2obobo6bobo2bobo4b2o8b2o8b7o4bo6bo5bobobo4b2ob2o6b2o2b2o8b2o7b5o6b10o4b10o20bo18bobo4bobo10bo12bo4bo15b3obobo2b3o6b2obobo29bo5b3o10bo2b4obo8b3o10b4o$12bob3o3b2obo5b2obo13b2obo14bobo8bobo4bo8bo36bobo6bobo6b3o2b3o6bo3bobo3bo7b2ob2o6b3obo3bob3o2b3obo3bob3o3bob3ob3obo3b3obo3bob3o23b2o3bo4b2ob2o2bo2b2ob2o8bo8bo13bo6bo16b2o2b2o3bo6bo4b7o5bo2bo5bo2bo7b7o4b2o2b2o2b3o6b3o4b7o6b2o3bo4b2o3b5o3b2o4bo2bo2bo2bo3b2o8b2o7bo2b3o2bo5b4o9bo6b2ob2o5b2o4b2o6bob2o6b5o7b2ob2ob2o6b2ob2ob2o21b2o17b2o6b2o4bob3obob3obo5bo6bo14b2o2bobo3bo8b2obo30b2o17bo7bo5bo3bo10bob2o2bo$12b2o5b6o3b6o5b2o4b6o7b2o21b4o4b4o35bo10bo7bo4bo7bo3bobo3bo6bo5bo8b2o3b2o8b2o3b2o6b2o7b2o6b2o3b2o7b2o5b2o16b2o4bo2b2ob2o2bo6b3o12b3o6bob3o4b3obo13b2o2b2o14b2o2bo2b2o3b3o5b3o2b3o4b2o2bo2b2o3b2o2b2o3bo8bo4b2o2bo2b2o7bo3bo6bobo3bobo6bo2bo4bo2bo3bo8bo8bo7bo4b2o2b2o7bobo4b3ob3o3b2o2b2o2b2o15bo3bo7b3o2b3o6b3o2b3o22bo19bo4bo6b3o2b3o2b3o3bobo6bobo11bo2b2ob4obo4b4o40bo12bo3bo2bo6b3o10bob2o4bo$11bo3bo4bo4bo3bo4bo3b4o4bo4bo5b4o21b3o4b3o36bobo6bobo4bob2o4b2obo6bo5bo8b2o3b2o6bo3bobo3bo4bo3bobo3bo3bo3bo3bo3bo3bo3bobo3bo4b4o3b4o6b4o11bobo5bobo6bo3b2o6b2o3bo7bo3bo2bo3bo16b2o20bo8bo2b2o18bo9b2o5bo8bo8bo10bo4bo7bo5bo7b2o2bo2bo2b2o3bo8bo9b3ob3o5bo4bo7b3o5bo3bo4b4o2b4o3b5o6b2obob2o8bo2bo10bo2bo23b2o21b2o10b2o5b2o30bo2b2o2b2o4bobo39bob2o11b2ob2obo10bo7bo2b2o2b2obo$12bo7bo8bo9b2o5bo11b2o24bob2obo26b4o8b3o6b3o6bo6bo24bo3bo10bo3bo10bo3bo7bo3bobo3bo7bo3bo8b2o5b2o11b2o12b2ob2o11b2o10b2o7bo2b3o4b3o2bo12b6o16b5o4b5o18b5o5b6o5bo4bo8b5o7b2o2bo23bobo6bobo5b6o22bobo2bobo8bo5bo3bo6b6o6b3obo5bo5bo5bobo4bobo4bobo4bobo17b7o16b2o4b2o8bo2bo2bo28b3o2b2o8b3obo38b2obo11b2o2bobo5bob2o2bo5bo2b2ob3ob2o$23bo8bo6b2o8bo8b2o21bo2b6o2bo23bo2bo10bob4obo6bobo6bobo23b3o11b5o10b5o12bo12b5o8b2o5b2o6b3ob2o10bobo5bobo8bobobob2obobobo6bo3b3o4b3o3bo12bo2bo16bo2bo2bo4bobo4b2o6b2o4bo2bo2bo5bo2bo5bo6bo6bo2bo2bo6bo2bo11b5o9b3o4b3o7b4o14bobo7bo4bo6bo7bobobobo5bob2obo5bobo3bo5bobobo10b2o12b2o22bo24b2o11bo2bo2bo27b2o2bobo13bo41bo15bo5bobob4o5bobo4bobo$32bo5bo2bo15b4o23bo4bo41b6o7b4o4b4o23bobo41bobobo22b4o3b4o8b3o9b3obobobob3o5bo2bo2b2o2b2o2bo2bo3bob2o2b3o2b3o2b2obo11bo2bo16b3ob3o4bo2bo4bo6bo5b3ob3o5bo2bo4bobo4bobo5b3ob3o7b6o7b2obob2o8b2obo2bob2o5b2ob2ob2o21b2o4b2o5b3o6b5o6bo4bo6bob2ob2o3bobobobo6b2ob2ob2o6b2ob2ob2o20b3o34b7o26b6o11b2o2b2o39bobo23bo2bo6bo2bo$23b2o7bo6b2o8b2o6b4o22b3o2b3o41bo2bo9bo8bo24bobo26b2ob2o10b5o22b4o3b4o5b3o2b2o8bo4bobo4bo6b4obob2obob4o5bo2b2o8b2o2bo11b2o2b2o16b2ob2o5b3o5b3o2b3o6b2ob2o5b2o2b2o2bo10bo5b2ob2o6bob2o2bo9bo3bo8bo3bo2bo3bo4bobo2bobo19b5o2b5o3bo17b4o2b4o8bobo5b3o10b4o10b4o22bobo18b8o43bob3o2bo9bob2o61b2o2bo12b2o2bo$22bo9bo6b2o7bo82b2o2b2o8bo2bo2bo2bo40bo12b2ob2o11bobo12bobo25b2o2bobo6b2o2b2o3b2o2b2o4b3ob2o2b2o2b2ob3o3b3o14b3o12b2o17bo2bo2bo4b3o5bo6bo5bo2bo2bo6b2o4bo10bo4bo2bo2bo8bobo9bobobobo9bobo2bobo8bo2bo22b2obo2bob2o4bobo6b5o6b2o2b2o11bo6bobo70b10o8b5o25bo4bo4bo9b3obo58b2obo2b3o8bo3bobobo$22b3o58b8o40bo4bo11b4o43bo12b2ob2o11bobo12b3o24bob3o3bo7b3obobob3o6bob2o3bo2bo3b2obo12b2o20bobo19b3o7bobo4b2o4b2o7b3o7bobo5b2o6b2o7b3o12bo2bo7b5o11bo4bo34bob2o4b2obo4bob2o6bo7bobo2bobo6b2o22bo2bo10bo2bo18b3o39b5o25bob2ob4o10bo2bobo60bo3b2o8bob3o3b2o$22bobo24b2o34bo2bo41bob4obo11b2o44bo12b2ob2o7bo3bobo3bo7bo3bo23b3o2bo2bo5bo2bobo3bobo2bo6bobob2o2b2obobo13b4o20b2o18bo3bo8bo5bo4bo7b2ob2o7b2o6bo6bo7b2ob2o12bob2o19b2obob2obob2o32bobo4bobo8b2o4bobo20b2o9b3o11b2o12b2o44bo6bo11bo28bo2b2ob2o11bo2bo59bobo4bo9b3o3bobo$24bo23b2o36b2o42bo6bo10b4o43bo14bo8b2ob2o3b2ob2o4b2ob3ob2o26bob2o5bo4b2ob2o4bo10b6o14b2ob4ob2o37b5o16b2o8bobobobo16bo2bo8bobobobo5b3o3bobo5bo2bobo2bo5b3ob6ob3o32b3o2b3o6bo2bo6bo5bo4b2o4bo4b2o8b5o10b2o12b2o19b3o21b2obo2bob2o10bo25b2o6bobo8bobob2o60b4o8b2o2bobo2b2o$21bo28bo32b2o4b2o38b2obo2bob2o10b2o56bo5bo6b3o5b3o6b3ob3o24b2ob4o6bo2bo5bo2bo4bo3b3o2b2o2b3o3bo5b14o15bo18bob3obo4b2o6b8o6b2ob2o7bo7bobo2bobo7b2ob2o6bobobobo2bo5b7o8b2o2b2o2b2o33bo8bo6b2obo12b4o2b4o7bo7bo3bo7bob4obo7bo4bo19bo23bo4bo11bobo27b5obo8b4o2bo56bo2bo3b2o7bo2bo$21bobo23b2o35bo4bo39b3o4b3o68b3ob3o6b2obo3bob2o6bo5bo24b2o2bo3bo3b2o2bo5bo2b2o4b2o3b2ob2ob2o3b2o6bo5b2o5bo14bo31bo6b2ob2ob2o17bo9bo4bo20bo4bobo6b2o3b2o8bo8bo34bo6bo7b2obo4b3o7b2o2b2o8bob2o4bo5bo7bob2obo7b3o2b3o17bob2obo63b2o4b2o12b5o56b3o2bobo5b2o2b2obo$20bo2bo23bobo34b2o2b2o59b2o56b3ob3o6b2obo3bob2o8bobo26b2o2bo2bo7bo7bo7b2o3bobo2bobo3b2o35bobo16bo5bo5b2o6bo4bo7b5o7bobo6b2o2b2o8b5o21b2o3b2o8b3o4b3o49b3o12b3o6b3o4b2ob2o3bo2bobo2bo6b2o2b2o6b3o4b3o16b2o2bobo35b3o24b3ob2ob2o9b2o4bo56bob3obo6b3ob2o2b2o$21bobo22b2ob2o32b2o4b2o37b5o2b5o9b2o55b2o5b2o6bo7bo8bo3bo26bo2bo2b2o4b2o9b2o4bobo2b3o4b3o2bobo6bo4b2o4bo16bob2o16bo3bo5bo9bo2bo8bo3bo7bob2o3bo2b4o2bo6bo3bo10bobobo7b2ob2o13b2o68bob2o4b2obo4b3o4b2obobobob2o4bo2b2o2bo5b2obo2bob2o18b2o2bo18bob2obo10b2ob2o19bo2b4o17bob2o56b2o2b3o5b2o2b2ob2obo$22bo23bo3bo78b3o4b3o10b2o54b2obo3bob2o3b4o5b4o6b2ob2o24bob2obo2bo5b3o7b3o6b6o4b6o9b2obo2bob2o15b2o2b2o16bo3bo8bo5bob2obo7bobobo5b2o2b2o2bobo6bobo5bobobo9bob2o26bo2bo60bobo5bobo4bobo12b4o3b4o3bob6obo4b3o4b3o18b6o16b2o4b2o9b2ob2o19bob2obo2b3o14b3o57b2ob2o6bobo2bo2bo$48bo80bobo4bobo10b2o55b2o5b2o4b3o7b3o5b3ob3o23b7obo7bo7bo9b2ob2o4b2ob2o10b3o4b3o15b2o32b2o17b2obob2o4b2o6bobob4obobo4b2obob2o7bobo9b2o5b2o10bo2bo52bo7b3o22bo7bo3bo7bo6bo4b2o8b2o17b2ob2o17b2o4b2o9b2ob2o19bo3bo2bobo17bo57bo9b3o4bobo$47bobo78bob2o4b2obo66b2o5b2o24bobo25bo5bo6b3o2bo3bo2b3o6bob2ob4ob2obo8b2o3b4o3b2o14b2obo28bobo3b2o6b2o3b2o5b2o4b2obo4bo2bo2bo2bo4b2o5b2o6bo2bo7bob2obob2obo9b4o50b3obo5bobo5bo8bo8b2o3bo3bo3bo4bob2o2b2obo4b2o6b2o17b2o21b8o9b5o19bo3b3obo2bo15bo56bo9b3obo2b3obo$46bo3bo79b3o2b3o81bob4ob4obo5bo5bo22b2obob3o5b3o2bo5bo2b3o7bo2b4o2bo11bo3bo2bo3bo14b2o31b2o4bo3b2o3bo4bo5bo4b2o8bo2b2o2bo6bo5bo7bo10bo4bo4bo64bobo5b2ob2o22bo5bobobobo7b6o5bo10bo17bob2o18b2ob2ob2o9bo3bo17b2ob3o3b4o17b2o52b2obo16b4o$47b3o80b8o68b2o5b2o4bo2b2o3b2o2bo6b5o23bo6bo6b3o9b3o7bo10bo10bo2bob2obo2bo15b4o30bo4b2o4b2o4bobo3bobo4b4o4bobo4bobo4bobo3bobo6bobo9b2ob3ob2o10b4o49b3ob3o2b2o3b2o3b3o4b3o7bo9bo9bo6bo7bo4bo21bo19b2o6b2o7b2obob2o16bo2b2o2b2o2bo15b2o50b3obob2o8b2o3b2o3bo$47bobo80bobo2bobo68b2o5b2o5b2o2bobo2b2o6b2o3b2o23bobo10bo13bo6bo3bo4bo3bo8b3o8b3o15b3o27b3o6bo4bo4b2o7b2o4b3o8b2o7b2o7b2o3b2o2b2o7bo9bo9bo2bo51bob2o5bobo6b2o4b2o7b2o19bo6bo7b2o2b2o23bo16b3o2b2o2b3o7bo3bo19bobo2bob2o16b3o48bo3bo2bo9b2o4b2ob2o$131b6o69bobo3bobo5b2o3bo3b2o6b2o3b2o26bo7b4o11b4o4b3ob2o2b2ob3o8bo2b8o2bo13bo3bo27bo6bo8bo2bo9bo2bo3bo5bob4obo4bo9bo3b5obo8bo5bo11b4o50b2o3bo13bobo2bobo5b2obo18b2obo2bob2o4b2obo2bob2o19bo36bobobobo19bo6bo16b2ob3o45b2o16b2o2b3o$130bo6bo83bobobobobo8bobobo26bo3bo4b3obo9bob3o6bo2b4o2bo10bobob2o2b2obobo14bobo36b2o4b2o4bobo3bobo4bobo7b6o6bobo3bobo6bob2obo5b4o3b4o8bo4bo52bobo3b2ob2o6bo4bo7b2o20bob4obo5bo2bo2bo2bo21bo32b3o5b3o14b2o2b2obobo16b2o2bo44b5o11bobo2bobo2b2o$131bo4bo86b2ob2o9bo5bo24b2ob2o7bo2bo7bo2bo8b2obo2bob2o11b2ob2o2b2ob2o67b2obob2o14b2o4b2o6b2obob2o11bo6b4o3b4o6b2ob4ob2o47b4o5bobobo6bo4bo8b2o18bobob2obobo3bobo6bobo58bo19bobo2b3o17bo4bobo42b2o2b2o9bo3b2ob3ob2o$221bob2ob2obo8b5o36bobo2bo5bo2bobo10b4o12bo2bob2o2b2obo2bo13b3o37bo4bo5bo3bo3bo3bob2o6b3o2b3o5bo3bo3bo4b2ob2o2b2o20b2o3b2o3b2o45bo2bo7b3o8b4o8b3o31bo2bo4bo2bo18b2obo31bobob3obobo18bo19b2obo3bobo41b2ob2o9bob2o3bo4bo$222bob3obo8b2o3b2o23bo3bob2o5bo3bo5bo3bo8bob6obo9b6o4b6o13bo39bo4bo7bobobo5b5o6bo4bo8bobobo6b2obo4bo5b3o3b3o7b2ob4ob2o47bo21b2o9bo22b6o7b3o2b3o18b2o37bobobobo18b2obobo16bo3bo3bo40bo2b2o11b3o5bo$222bo2bo2bo8bo5bo22b2o2bobobo8bo7bo10b2o3b2o3b2o8bob4o4b4obo12b3ob2o33bobo4bobo5b2ob2o5bob2o6b3o2b3o7b2ob2o5b2obo3bo7b3o3b3o8b2ob2ob2o49bobo7bo10b2o9bo3bo15b4o4b4o5bob2obo19bobo35b2o2bo2b2o17bobobo20bo61bob4obo$222bobobobo8bo5bo23b4o2bo9b2o5b2o9b2obo6bob2o8bob2o2b2o2b2obo15bobo34bo8bo4b2o3b2o5b3o6bo2b2o2bo6b2o3b2o5b2ob4o5b5o3b5o5b4o2b4o49b2o5bobobo19b4o18bob4obo6bo2b2o2bo57b2obob2o16bob2obo18b2ob2o43b3o14bob6o$225bo11b7o23bob3o2bo28b2ob4ob2o13bo2b2o2bo19b3o34b2o4b2o15b2obo6bo2b4o2bo6b2ob2o9bob2o6bo3bobo3bo8bo4bo68bobo2bobo5bob2ob2o16bob4obo6b2o4b2o20b2o33bo2bo3bo2bo13bobo2bo20b2obo42b2o16b5obo$224bobo8bobob3obobo28bo10bo3bo13b2o2b2o2b2o9b2o4b4o4b2o51bobo4bobo5b5o7bobo5bo6bo5b2o5b2o6bob2o6bo3b2ob2o3bo4b2o2bo2bo2b2o47bobo15bo2b2o2bo6bobob2o18b4o8bobo2bobo21b3o54bobob3o19bo2bo40b2obo18bo2b3o$222b7o5b2o2bobobo2b2o27bo29b2ob2ob2o16bo2bo20b2o38bo2bo6bobo3bobo5bob2o4b2o4b2o6b3ob3o8b2o6bo4bo3bo4bo3b2obob2obob2o46b2o17bo2b2o2bo9b2o32bo4bo22b2o34b2o3b2o15bob2o22b2obo35b2ob2o17bo4b2o$221bo2bobo2bo4bob2o5b2obo27b3o6b2ob3ob2o8b2obo8bob2o13b2o72b3ob3o6bobo4b3ob2ob3o5b3ob3o7bo10bob2o3b2obo5bo2b2o2b2o2bo46bo2bo18b2o10bob3o29b2ob4ob2o19bobo56b2o24b3o34b5o19bobobobo$220bobobobobobo4bobo5bobo28bob2o7bo3bo11bo3bo4bo3bo9bobo6bobo14b2o51b3ob3o8bo4bo2b4o2bo4bobo3bobo5b3obo7b3o5b3o8bo4bo51bo18b4o10b4o17bob2obo9b4o22b2o36b2ob2o15b2o23b3ob3o32b5o18bo2b2o$221bobo3bobo39b6obo5bo3b3o3bo6b2o3bobo2bobo3b2o8b2ob4ob2o17bo50bo5bo5b2o7b8o7b2ob2o8bob2o6b2o9b2o3bob4o2b4obo45bob2o15b3o2b3o8bo19bobo2bobo8b4o23b2o34bo5bo13b3o23b2o2b3o32b3o19b2o$222bo5bo5bobo7bobo24b4o2bo5bo2bobo2bo7b3o3bo4bo3b3o7bobob4obobo14bob2o48bobo3bobo5bo7b8o7bo3bo8bobo24b2o8b2o46b2o18b2o2b2o7bobo18bob6obo5b2o4b2o20bo38bobo14b2o2bo21bobo2b2o49bo$234bo2bo5bo2bo25bo2bo7bo2b3o2bo8bo3b2o4b2o3bo7b6o2b6o14bo51bo5bo6b2o5b2o6b2o19b2obo6bobo7bobo7bo4bo48b2o19bo4bo7b3o17b4o4b4o3b2o2b2o2b2o17bob2o36bo3bo14b5o21bo2bobo50b4ob2o$238b2ob2o30bo12bobo11b3obob4obob3o7bo12bo14b2o69b2o2bo2bo2b2o4b3ob3o11bo7b2o5b2o8b2o4b2o66b3o4b3o4b3ob3o14b12o4b2o4b2o19bo35bo2bo3bo2bo35bo3bobo49bo2b2obo$237bobobobo30bo8bob2ob2obo9bo2bob4obo2bo9b12o15bo64bob2o3bo8bo5b3ob3o8bobo8b3o3b3o9b2o2b2o67bob2o2b2obo4b4o32b10o20bo32b2o9b2o7bob2o23bobob2o51b3o3bo$236b2ob3ob2o26b5obo4b2ob5ob2o10bobo4bobo12b4o2b4o15b2obo64bo3bobo6bobo5b2ob2o9b2o10bobobobo9b2o4b2o67b2o4b2o7b3o18bob4obo5b3ob2ob3o20b2o32b3o5b3o6b2ob3o21b2o2bobo51b3o3b2o$238b5o29bob2obo5b2o5b2o11bobo4bobo11bo2bo4bo2bo16b2o63bo5b2o6b2o6b2ob2o20b4ob4o7b2o6b2o67b6o7bo2bo20bo2bo9bob2obo20b3o32bob2o5b2obo4b3o24bob2ob2obo49b2o2bo3bo$238b2ob2o28b2o3bo4b2o9b2o29b3ob2o2b2ob3o13bo2bo63bo6b8o6b7o8bo12b2ob2o9b4o2b4o66b2o4b2o7bo19b3ob2ob3o4bobob2obobo19b2o35b3ob3o5b2o4bo20bo2b2o2bobo48bo5bob3o$238bo3bo27b3o8b2o9b2o8b3o6b3o13bob2obo18b2o63bo7b2ob2ob2o6bobobobo7b3o10b2o3b2o85b6o8bo21b6o9b4o58bob2ob2obo3bo3b4o21b2ob2o2bo50b2o3b2o$238bobobo27bobo8b2o2b2ob2o2b2o9b10o8b3o2bob4obo2b3o12b2o64b2o4bobo4bobo20b2o12bobo12b6o69bo4bo7b2o21bo4bo7b2ob2ob2o19bo39b3o8b2o2bobo19b2o3bo51bob3obo$237bo2bo2bo26b3o13b3o13bo2b6o2bo7bo2bobobo2bobobo2bo14bo64b2o3bob2o2b2obo7b3o11b3o8b3ob3o9b8o68bo4bo8bobo17bo2bo2bo2bo73bo8bo2bobo23bo4bo51bo3bo$269bo12bob3ob3obo9b3ob4ob3o11bob2o2b2obo18bo65bo4b2o4b2o34b5o10bob4obo68bo4bo7bo3bo18bo4bo6b3o4b3o17bobo38b3o12bo19b2ob2o55b4o$238bobobo25bo2bo2bo8b2obobob2o12bobo2bobo15bob2obo19bobo62bo8bo2bo8bobobobo9b2o9bo2bo2bo10bob2obo82bobo22b2o9bob4obo19bo50b2obobo19bo3bobo47bo3bo3bo$239bobo26bo15bobobobo11b4o4b4o12b2ob2ob2o18bo63b3o33b2o11bo2bo2bo9bobo2bobo68bo4bo8bob2o15bob3o2b3obo3b2o2b2o2b2o17b3o47b4obobo19bobo2bo47bob2obo$268bo2b2o9bo2bo3bo2bo10bobo4bobo14b2o2b2o17b3o71b2ob2ob2o5b2obobob2o5b2obobo8bo5bo9b3o2b3o67b3o2b3o7bo18bo2b2o2b2o2bo3bo8bo17b3o46bobo2b3o25bo45bo4b2o$270b2o10b4o3b4o12bo4bo15b2o4b2o17bo63bo8b8o6bo5bo7bo12bobobobo9b3o2b3o67bo6bo10bo20b2o12b2o21b3o47bo29bobo46b2o3bo$270b2o11bobo3bobo11b3o4b3o12b4o2b4o15b2o64b2o6b8o18b3o12b2obob2o7b4o4b4o64bob2o2b2obo6b2obo20b2o10bob2obo20bo47bob3o24b4o46bo2bo2bo$282b2obo3bob2o9b2o3b2o3b2o10b2o2b4o2b2o16bo60b2o2bo50bo9b4ob4ob4o64bo2b2o2bo10b2o16bobo2bobo9b2o68b4o26bob3o44b6o2bo$283b2o5b2o10b4o4b4o11bob6obo17bo61bo2b2o31b4o10b2obobob2o5b2o2bob2obo2b2o65b2o2b2o7bobo22b2o11bo2bo68bobo24bobo2b2o43b2obo3bo$282b5ob5o11bo2b2o2bo11b4o2b2o2b4o17bo62bo33bo2b2o8bo7bo10bo2bo71bo2bo8bo2b2o32b2o2b2o67b2o25bo2b3o45bo3b3o$282bo2bo3bo2bo11bo2b2o2bo12bo2b2o2b2o2bo15b2ob2o95bo2b3o7bobo3bobo6bo2bo4bo2bo68b2o48b2o67b2o2bo22b4ob4o41b2o3b4obo$283bobo3bobo12bo6bo12bobobo2bobobo18b2o59bobo34bo3bo7b2obobob2o6b2ob2o2b2ob2o78b2o37bo2bo66b3obo21b4o2bobo43bo2bo2bo$283bobo3bobo12bo2b2o2bo12bob3o2b3obo79b2o33bo3bo12bobo9b2o2bo2bo2b2o117bo2bo66bob2o23bo51bo2b3o$284bo5bo13b2o4b2o13b2o6b2o17bobo58b2o36b4obo6bo3b3o3bo5b5o2b5o78bobo35bob2obo68bo21bo2bo47bob2o$282bobo5bobo12bo4bo16bo4bo19b2o60b2o33bob2o11b9o5b5ob2ob5o116b4o61b4obo24bobobo44b2obob2obo$284bo5bo15bo2bo41bo62bo37bo10b2o3bo3b2o8bob2obo81b4o34b2o2b2o60bo2b2o2bo22b5o43bo2bo$305b2o2b2o14bo2bo2bo2bo115bobobo8bob3ob3obo7bobo2bobo183bo2b3o2bo22bobo45bo3b3o$282bobo5bobo12bob2obo13b2ob2o2b2ob2o118bo9bo7bo9b2o2b2o183bo2bo3b2o21bob2obo43b2ob2o$283bo7bo12b2o4b2o12b2obo4bob2o118bo9bobo3bobo9bo4bo81bo102b2o3bo23bo5b2o38b3ob4o$282bo9bo11b2o4b2o11b3o8b3o115bo2bo9b2o3b2o12b2o82b2o38b4o61b2obo25bobo2bo43bobo$283bo7bo13bob2obo15bo6bo119bo13bobo13bo2bo82b2o36b6o57bobo3bo25b2ob4o40b2ob2o$299b3ob3o4b3ob3o7bo2bo4bo2bo116bobo10bo5bo9bobo2bobo79b2o37b2o2b2o61bo25bo2bo2bo40b3ob3o$283b2o5b2o7bobo4bo2bo4bobo7bo10bo118bo12bobo10b4o2b4o79bo36b3o2b3o57bo2bo25bob3o2bo38b2obob2o$282bo9bo5bobobob8obobobo8bo6bo123b2o6bo5bo7b2o2bo2bo2b2o80bo99b3o28b2ob2o40b2o$282b2o7b2o6b2ob2obo4bob2ob2o6b2o10b2o117bob3o6bo5bo11bo2bo84b2o35b4o57bobo2bo26b3ob2o36b2o2b2o$300b4obob2obob4o5bobobo8bobobo115bob4o4bobo3bobo5bo3b2o2b2o3bo78bo37b4o58bobo27bob2o2bo35bo2b2o$281bobobo3bobobo7b6o2b6o7bo2bo8bo2bo117b3o5bob2o3b2obo5bob2o4b2obo79b3o35b4o57bo31b3obo37b3o$282bobo5bobo7bo2bo2bo2bo2bo2bo6b2obo8bob2o116bo4bo4b2o5b2o5b3o8b3o78b3o35b4o59b2o28bobo36b6o$281b3o7b3o9bobo4bobo9bo14bo125bob2o3b2obo95bo2bo35b4o56b4o30b2o38b2o$303bobo4bobo11bob2o4b2obo120b2o6bobo3bobo6bo4b2o4bo78b3o35bo4bo55b2ob2o65bobo2bo$302bo3bo2bo3bo11b2o6b2o121bo9b2ob2o10b2ob2ob2o80b5o33b2o2b2o52bo5bo32b2o35bo$301bobo2bo2bo2bobo9bobo6bobo119bo7bo9bo7b2o4b2o84bo33b2o2b2o50bob3obo35bo31b2obo$301b2obo6bob2o9bobob4obobo118bobo4b2obo7bob2o4b2ob4ob2o78b2o3b3o30b3o2b3o46b2o3bob2obo31b2o30bob3o$303b2ob4ob2o10b2o3bo2bo3b2o117bo6b2obo7bob2o92b8o31bob2obo47b3obo4bo34bobo26b3ob3o$303bo2b4o2bo10b3ob2o2b2ob3o117b2o7bob2o3b2obo8b2o2b2o81b6o33b4o48b4o4bo33b2obo26bob2ob2o$305bo4bo17b4o122b2o7b2ob2ob2ob2o5b2o2bo2bo2b2o117bo2bo46b6o39b5o21b2o6bo$307b2o15bo4b2o4bo130bo3bo9bo3b2o3bo80b2o35bo4bo44bo4bobo36b2obo24bo2bob2obo$305b6o14b3o4b3o132bobo9b4o4b4o78bob2o35b4o44bobo3b2o36bo3b3o20b2o7bo$305b2o2b2o12b2ob2ob2ob2ob2o114b4o10bo5bo7b5o2b5o80b2o82b2obo2bo37b2o3bo22b3o4bo$304b2o4b2o10b2o5b2o5b2o113b2o2b3o6bo2bobo2bo6b2o3b2o3b2o79b2o81bob2obo39b2obo32bo$303bob6obo9bob2o8b2obo115b3o7b2o2b3o2b2o6b3ob2ob3o79bob2o79bob2o3b2o36bo3bo24bo3bo2bobo$302bo3b4o3bo8bo14bo118b3o5bo7bo6bo2bob2obo2bo81bo79bobo2bo41b3o23bo2bob3o$301bo12bo6bob2o10b2obo116b2o7b2o2bo2b2o6b2obo4bob2o80bobo77b2obobobo39bo2bo23bob2o2b2o$302bo10bo7bobobo8bobobo117b3o6bo5bo7b4o4b4o81b3o76bob3obo40b3o2b2o17bo3b2o$301bo12bo7bob3o6b3obo118bo21b2obob4obob2o78bobo78bo2bobo42bo3bo19b2ob2obo$301bo12bo10b2o6b2o121bo7b3o3b3o6bo10bo80bo3bo75b4o44bo2bo19b2obo$301bobo8bobo10b2o6b2o121bo8b2obob2o6bo2b8o2bo78bobo75b3obo43b3o3b2o17b2o3bo$300b2obo3b2o3bob2o8b3o6b3o119b2o8b2o3b2o6b2o10b2o79bo126b3o19bo3b2o$301b3o2b4o2b3o139bo3bo19bo12bo78bo76bo2b2o47b2o2b2o14bob2o2bo$300bob4ob2ob4obo7b2o10b2o119b3o6b3ob3o6b2o3b4o3b2o78b2obo71b2obo2bo46b2o3b2o16b2o$301b14o8bobo8bobo117bo2bo8bo3bo9bob2o2b2obo81bo76bob2o47b4o13bob2obo$303bobo4bobo8b2ob2o8b2ob2o116b4o6b3ob3o9bobo2bobo156bo3bo47b3obo14b6o$303bo8bo8b2o2b3o4b3o2b2o117b3o7bobobo10bobo2bobo82b3o72b2o48bob2o16bobobo$302bob8obo9b3o8b3o117bo10b3ob3o99b2obo67b4obo48bo18b2obo$304bo2b2o2bo11bob3o4b3obo117bo9bob2ob2obo96bo4bo66b4o2b2o44bo4bo16b2o2bo$304bo2b2o2bo12bo10bo116bobo6b3obo5bob3o94b3o67bo7bo43b3ob2o15bobo$307b2o15bo2bo4bo2bo114b3o2bo5b2o11b2o93b2obo68bo5bo43bob6o9b2o2bob2o$305b6o11bo3bo6bo3bo113bo3b3o7b2o3b2o98bo70bo3bobo43bo2b2obo11b3obo$306bo2bo13b2obo6bob2o114bo3b2o7bob2ob2obo96b4o65bo6bo46b2o13bo2b2obo$305bob2obo10b3o12b3o111b2o2b2obo6bobo3bobo95bob2ob2o64b2o4bo45b3o14bob3o$305b6o12b3o8b3o114bobo11b3ob3o98b2o66b3o3b2o45bo2bo11b3o3bo$305bob2obo12b2o10b2o116bo118b2o64b3o50b4o10b4o3bo$304bo6bo10b2o12b2o114bo119b3o65b2o52bo8bobobo4bo$305b6o11b2obo8bob2o113b4o183bobo48bob4o7bo2b2o2bo$307b2o14bob2o6b2obo114b3o234bob2o2bo5b3o4bob2o$305bo4bo11bo2b2o6b2o2bo113bo2bo117bobo61bob2o47bo3b3o6b2ob2ob3obo$304bo2b2o2bo11bo2bo6bo2bo117bo117b3o63b2o49bo3bo4b2ob2obobobo$305b6o12bo2bo6bo2bo114bobobo114bo2bo62bob2o45bob5o5bo$304bo2b2o2bo11b2o10b2o115bo2b2o112b5o63bo46bobobob2o4bo8b2o$305bob2obo12bobo8bobo116b2o114bo2b2o62b3o44bob2o2bo5b3o7bo$304b2o4b2o9b2obo2b2o2b2o2bob2o113b2o114b2ob3o109bo10bobo6bo$305b2o2b2o11bo4b2o2b2o4bo114bo116b2o62bob2o45b2ob2o7b2o7bo$306bo2bo12b5o6b5o112bob4o112bo3bo61bo46bobo3bo8bo6bo$305bo4bo11bo3bo2b2o2bo3bo116bo114bo2bo61bo44b6o8b2o2bo4bo$323b2obobo2bobob2o115b2obo116bo61bo43b2o2bobob2o5bo2bob2ob2o$322b2o4bo2bo4b2o115b2obo115bo59bobo43b3obo2bo8bobo3bo$327b2o2b2o119b3obo114bo60bo2bo41bobo6bo5b2obo3bo$452b3o176bo3bo42b2o10bobobo$325b2o6b2o116bo179b3o45bo11b3o$325b2o6b2o117b3o177b2o46bo4b3obobo$631bo56b4o$324bo2b6o2bo118b2o172b2o53b2o3b3o$324b3o6b3o118b3o170bo2bo52bobobo$325b2o2b2o2b2o119b2o170bo3bo50b2obo4bo$323bo3b2o2b2o3bo115bo2bo169bobo2bo51bo7bo$324bo3bo2bo3bo116bo2bo169b3o51bobo7bo$323bo4bo2bo4bo116bo2bo171bo50bobo4b3o$325bobo4bobo120b2o167b2o2b2o48b2o6b2o$326bobo2bobo119bo2bo167bo3b2o51b2obob3o$325bo8bo117bo2bo167b3obo53bobo2bo$326bo6bo120bo167b2o2b2o50bo4b2o$324bo3bo2bo3bo286bo3bo52bobo$324bo4b2o4bo116b2o169bo54bo$324bo10bo117bo169b3o48bo2bo$324bo3b4o3bo115bobo170bo50b2o$324bob3o2b3obo114bo171b2o$324bo2b2o2b2o2bo114b4o165b2obo49b3o$323bo3bob2obo3bo114b2o165bo2b2o45bo2b2o$322bo3bob4obo3bo113bo2b3o162bo47bo2b3o$323bo2b8o2bo113b7o161b2o46b2o2b3o$323b2o10b2o114b2obo211b2o4b2o$323bobobo4bobobo113b2o2b2o216bo$322bob2o2bo2bo2b2obo116bo210bobo2bo$323bo2b3o2b3o2bo117bo209bob2o2b2o$322b5o6b5o324bob5o2bo$322b2o2bo6bo2b2o115b2o207bo2b6o$322b2ob3o4b3ob2o117bobo207b2o$324bobo6bobo117b2o2b2o202b2obobo$452b3obo199b2obo2bo$452bo205bobobo$323bo12bo116b2o201bo2bobo$323b4o6b4o118bo198bobo2bob2o$322bo4bo4bo4bo116bobo197b3o4b2o$321b4o10b4o116b2o199bobob3o$322b3o10b3o116bo199bob3o$455bo197bob5o$322bobo10bobo115b2o198b2ob4o$320bo2b2o10b2o2bo311bobobobo$322b4o8b4o312b2o$324bo10bo314b3o$323bo12bo314b2o$321bo2bo10bo2bo306b4obo$323b2o10b2o306bo2b2ob2o$325b2o6b2o307bo2b4o$325bo8bo308bobo2bo$322b3o10b3o303b2o2b2o2bo$325bo8bo308b4obo$328b4o310bo$327b2o2b2o$326b2o4b2o$325b3ob2ob3o$323bobobob2obobobo$322b2o2bo6bo2b2o$321b2o3b2o4b2o3b2o$320bobo4b6o4bobo$320b2o2bobob4obobo2b2o$327b2o2b2o2$326b3o2b3o$324bo2b2o2b2o2bo$324b2ob6ob2o$327b6o$324bo10bo$325bobo4bobo$327bob2obo$325bo8bo$328b4o$328b4o$328bo2bo$327bo4bo$327bob2obo$326bo2b2o2bo$325bo2bo2bo2bo$325b2o6b2o$324bo10bo$326bo6bo$327bo4bo$323bobo8bobo$322bob2o8b2obo$322bobobo6bobobo$322bobo10bobo$324bo10bo$323bo12bo$322b3o10b3o$325b2o6b2o2$324b2o3b2o3b2o$324bo2b6o2bo$323bo2bob4obo2bo$323b2o2bo4bo2b2o$324b4ob2ob4o$324b2o3b2o3b2o$324bob8obo$323b3ob6ob3o$323bo12bo$324bobo6bobo$320b2o2bo10bo2b2o$323bobobo4bobobo$321bobo2bo6bo2bobo$324b2o8b2o2$323bo3bo4bo3bo$323bo12bo$325bo8bo$321bob2o10b2obo$321b3obo8bob3o$323bo12bo$323bo12bo$321b2o14b2o$323bo12bo$321b3o12b3o$321bo16bo$324bo10bo$323bo12bo$324bobo2b2o2bobo$323b2o2b6o2b2o$324bo2bo4bo2bo$326bobo2bobo$323b2obobo2bobob2o$323bo3b2o2b2o3bo$323bo2b3o2b3o2bo$326bo6bo$325bob2o2b2obo$327bob2obo$327b2o2b2o2$327bo4bo3$329b2o$329b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 3360 HEIGHT 1085 ZOOM 4 ]]
(click above to open LifeViewer)

the flocks

thank you to for Lapintra/TrollDu13EtDu14/Lapin Acharné for finding a surprisingly small 2c/8 in apgsearch,[1] which works in all three rules and has been proven to be minimal-width by ascendantDreamweaver

the dreamweaver also increased 2c/8 even (in which none were known previously) to 18, 16 (found), and 18, respectively

B3/S12 (Flock)

all partials for c/2 seem to be single-row irrespective of period, I conjecture there are no c/2's in this rule

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter-preserving
(1,0)c/3 11 21 22 23
20 (JLS) 27 (JLS) 28 (JLS) 27 (JLS)
(1,0)c/4 11 17 22 17
(1,0)c/5 10 < w ≤ 18 19 20 < w ≤ 24 21
(2,0)c/5 12 25[n 13] 24 < w ≤ 34 25
(1,0)c/6 10 17 < w ≤ 21 18 19
(2,0)c/6 10 19 20 21
(1,0)c/7 8 13 14 15
(2,0)c/7 9 17 18 19
(3,0)c/7 12 23 24 25
(1,0)c/8 7 13 14 15
(2,0)c/8 10[n 13] 17[n 13] 18 17
(3,0)c/8 10 19 20 21
(1,0)c/9 7 11 12 13
(2,0)c/9 8 13 14 15
(3,0)c/9 9 17 18 19

B36/S12 (HighFlock)

Velocity Asymmetric Odd-symmetric Even-symmetric
(1,0)c/3 11 < w ≤ 14 21 22
14 (JLS)[2] 29 [1] (JLS) 30 [2] (JLS)
(1,0)c/4 10 15 16
(1,0)c/5 9 < w ≤ 14 17 18
(2,0)c/5 11[n 13] 17 20
(1,0)c/6 9 15 16
(2,0)c/6 10 < w ≤ 15 19 20
(1,0)c/7 8 13 14
(2,0)c/7 9 17 18
(3,0)c/7 12 23 24
(1,0)c/8 7 11 12
(2,0)c/8 10[n 13] 13 16
(3,0)c/8 10 19 20
(4,0)c/10 8[n 14] 17[n 14] 14
(3,0)c/15 4 9 8

B38/S12 (Pedestrian Flock)

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter-preserving
(1,0)c/3 11 21 22 23
20 (JLS) 27 (JLS) 28 (JLS) 27 (JLS)
(1,0)c/4 10 17 22 17
(1,0)c/5 10 19 20 < w ≤ 24 21
(2,0)c/5 12 25[n 13] 24 < w ≤ 34 25
(1,0)c/6 10 17 < w ≤ 21 18 19
(2,0)c/6 10 19 20 21
(1,0)c/7 8 13 14 15
(2,0)c/7 9 17 18 19
(3,0)c/7 12 23 24 25
(1,0)c/8 7 13 14 15
(2,0)c/8 10[n 13] 17[n 13] 18 17
(3,0)c/8 10 19 20 21

B3ai4/S23

Velocity Asymmetric Odd-symmetric Even-symmetric
(1,0)c/2 12 23 24
(1,0)c/3 10 21 22
(1,0)c/4 10 19 20
(2,0)c/4 11 21 22
(1,0)c/5 9 17 18
(2,0)c/5 10 19 20
(1,0)c/6 8 15 16
(2,0)c/6 10 < w ≤ 15 21 20

B34kz5e7c8/S23-a4ityz5k (yujh rule :-)

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter-preserving
(1,0)c/2 11 11 24 11
15 24
(1,0)c/3 11 11 20 11
11 17
(1,0)c/4 9 9 16 13
(2,0)c/4 5 11 12 11
14 13
(1,0)c/5 8 17 18 17
20 19
(2,0)c/5 11 19 20 < w ≤ 26 21
(1,0)c/6 10 17 18 19
(2,0)c/6 10 17 20 19
(3,0)c/6 10 15 20 19
(1,0)c/7 8 15 16 17
(2,0)c/7 9 17 18 19
(3,0)c/7 10 19 20 21
(1,0)c/8 7 13 14 15
(2,0)c/8 8 15 16 17
(3,0)c/8 10 19 20 21
(4,0)c/8 7 11 14 13
(3,0)c/9 8 < w ≤ 17 13 16 15
(5,0)c/10 8 15 < w ≤ 21 16 15
(6,0)c/12 7 11 14 13
(7,0)c/14 6 11 < w ≤ 19 12 13
(11,0)c/22 5 7 < w ≤ 17 8 9
(12,0)c/24 4 7 < w ≤ 21 8 < w ≤ 24 9
(10,0)c/26 4 < w ≤ 7 7 8 9
x = 495, y = 70, rule = B34kz5e7c8/S23-a4ityz5k 76bo9b3o6b3o5b3o3b3o5b3o5b3o5b3o11b3o5b3o4b3o3b3o4b3o4b3o4b3o3b3o7b3o14b3o6b3o3b3o8b3ob3o13b3o2b3o7b3o7b3o9b3o2b3o13b3ob3o11b3o7b3o8b3o2b3o9b3ob3o10b3o6b3o11b3o4b3o7b3o5b3o7b3o10b3o8b3o3b3o$6b3o5b3ob3o5b3o5b3o5b3o14b3o5bo7b3o8bobo6bobo4bo2bo3bo2bo3bo2bo5bo2bo4bob4o5b4obo5bo2bo3bo2bobo2bo4bo2bo2bo2bo3bo2bo3bo2bo6bob2o12b2obo6bob2ob2obo7b2obobob2o11bo8bo5bo2b3o3b3o2bo7bo8bo11b2obobob2o11bo9bo11b4o13bobo13bo8bo13bo4bo2b2o5b2o2bo3bo2b2o5bo2b2o8b2o2bo4bo3bo5bo3bo$6bo2bo3bo2bobo2bo3bo2bo5bo2bo3bo2bo14bo2bo3b3o4bo2bo2bo6bob2o4b2obo6b2o3b2o4bo3bob3obo3bo2b2o2bo2bo3bo2bo2b2o4bob2o3b2o5b2o4bo8bo5b2o3b2o8bo2b2ob2o4b2ob2o2bo5b2o2bobo2b2o4b2obo5bob2o8b2o8b2o5bo3b2ob2o3bo7b2o8b2o8b2obo5bob2o27bo2bob2obo2bo5bo2bo3bo2bo21bo7bo7bo2bo7bo2bo3bo2bo6bo2bo10bo2bo2b3o13b3o$2b3obo3bobo3bobo3bobo3bob3obo3bobo3bob3o6b3obo3bob2obo4b3ob3o5bobob2o2b2obobo6bo3bo5bo2b2obobob2o2bo2bobobo3bobo3bobobo3bo7bo7bo6bo4bo8bo3bo9b3o4b2o2b2o4b3o5bobo5bobo2b2obobo5bobob2o3b4obob4obob4o7bobo9b4obob4obob4o3b2obobo5bobob2o4b2o3b2o3b2o3b2o4b3o6b3o5b3o5b3o6b2o3b2o5bo2bo7bo2bo4b2o3bo3bo3b2o3b2o3bo4b2o3bo6bo3b2o4bo13bo$bo2bob2o2bobo2b2ob2o2bobo2b2obobob2o2bobo2b2obo2bo4bo2bob2o2bob3o5bobobobo6bo3bo2bo3bo4bo9bo4b2o2bobo2b2o6bobobobobobobobo17bo21bo9bo7bob2o3bo2bo3b2obo24bo5bo8bo3b2o2b2o2b2o3bo3b2o2bobo2b2o5bo3b2o2b2o2b2o3bo8bo5bo9bo2bo2bo3bo2bo2bo2b2o12b2ob2o11b2o4bo2bo2bo8bo7bo9b2o7b2o7b2o8b2o10b2o6bo2bo7bo2bo$o3bo2b2o5b2o3b2o5b2o2bobo2b2o5b2o2bo3bo2bo3bo2b2o4bobo17bobobo2bobobo6bo5bo5bobo2bobo2bobo5bob2o2bobo2b2obo15b5o21bo5bo10b4o2bo2bo2b4o22b2o2b2ob2o2b2o5bo3bo8bo3bo6b2ob2o8bo3bo8bo3bo5b2o2b2ob2o2b2o7bo3bo5bo3bo5bo10bo5bo9bo5b2o5b2o4bobo9bobo5b3o7b3o5b3o7b3o10b3o5bo4b2ob2o4bo$o2b2o2bobo3bobo3bobo3bobo2bobo2bobo3bobo2b2o2bo2bo2b2o2bobo24b2ob4ob2o7bo5bo7bob2ob2obo6b2ob2ob2ob2ob2ob2o40bo5bo10bo14bo20bob3o2bobo2b3obo3bo2b2o8b2o2bo5b2o3b2o7bo2b2o8b2o2bo3bob3o2bobo2b3obo58bo7bo23bo3b3ob3o3bo3bo3b3o3bo3b3o4b3o3bo4bo5bobo5bo$2b2o23bob2ob2obo11b2o6b2o29b5o2b5o5b2o5b2o5bobobobobobo6bob2ob2ob2ob2obo15bo3bo20b2o5b2o7b2o3b4o2b4o3b2o19bo5bobo5bo25bo2bo3bo2bo27bo5bobo5bo4b2obobob2ob2obobob2o34bo2b2obob2o2bo2bo2bo7bo2bo4bo13bo3bo9bo16bo4b2o2bobobobo2b2o$bobo22bobobobobobo10bobo4bobo29b2o8b2o5b2o5b2o5bob2o3b2obo7b3o7b3o16bo3bo20b2o5b2o7b2obo5b2o5bob2o21b2o7b2o8bo12bo5bo2bo3bo2bo7bo12bo8b2o7b2o9bobo7bobo40b2obob2o5b2obo7bob2o53b3ob2obobob2ob3o$26bob2o3b2obo9b2o8b2o45bo7bo7bo5bo9b2o9b2o16b2ob2o20bo7bo7b2o2b2obo4bob2o2b2o20b2o9b2o25bo3bo3bo3bo27b2o9b2o7b2ob2o5b2ob2o37bobo2bo2bobo5b2o7b2o19bo5bo13b2o4b2o9b2o4bobo4b2o$28bo5bo10bo2bo6bo2bo28b3o4b3o5bo2b2ob2o2bo6bo5bo10bo9bo19bo21bo2b2ob2o2bo10b3o6b3o62b3o7b3o7b2o8b2o30bo9bo40bo7bo6bo9bo19b2o3b2o31bo2bobobobo2bo$28bo5bo9b2o12b2o28bo6bo6b3obobob3o5bobo3bobo7b3o9b3o14b7o18b3obobob3o47bo9bo29bo5bo9bobo8bobo8bo9bo60b2o7b2o5b2o7b2o20b2ob2o15bo4bo11b4obobob4o$27bobo3bobo6b2obob2o6b2obob2o41b2obobob2o8bo3bo13b3ob3o17b2o5b2o18b2obobob2o10b4o6b4o24bo9bo26bo2bo5bo2bo6bob2o6b2obo8bo9bo7b2o3b2o3b2o3b2o37b4ob4o6bo9bo21bobo14bobo4bobo9b2obobobobob2o$27bobo3bobo7bobo12bobo41bo3bobo3bo7b2ob2o13bobobobo17b2ob3ob2o17bo3bobo3bo7b3o12b3o20bo13bo23b2o3bo3bo3b2o3bo3bobo4bobo3bo4bo13bo6bo3bo5bo3bo38bobo3bobo7b4ob4o21bo3bo12bo3bo2bo3bo9bo3bobo3bo$41b3obobo8bobob3o39bo2bo3bo2bo8bobo14bobobobo18b2obob2o18bo2bo3bo2bo6b2o16b2o20bo11bo25b4obobob4o4bo3b3o4b3o3bo5bo11bo5b4ob4ob4ob4o40bo11bo2bobo2bo18b2o2bobo2b2o8b2o2b2o2b2o2b2o7bobob2ob2obobo$40bo8bo4bo8bo39b3o3b3o8bo3bo15bobo21b5o20b3o3b3o7b2o16b2o21bo9bo26bo4bobo4bo6b2obobo2bobob2o8bo9bo59b2o9b2o7b2ob2o19bo11bo7b3o2bo2bo2b3o5bobo2b2o3b2o2bobo$44b4ob2o2b2ob4o44b2o3b2o7b2o5b2o63b2o3b2o8b2o16b2o58bo11bo11bo2bo34bo9bo37b2o3bobobo3b2o6bo3bo18bo6bo6bo25bo5bo3bo5bo$42bo3b3obo2bob3o3bo44bobo9bo7bo38b3o24bobo9bo20bo20b2o7b2o26bob2o5b2obo11bo2bo12b3o7b3o57b2o11b2o4b2obobob2o17bo11bo8bo10bo$49b2o2b2o48bob2ob2obo6bo7bo62bob2ob2obo9bo14bo60b4ob3ob4o9bo6bo11b2o7b2o8bo52b2o5b2o7b2obobob2o18b3o5b3o9bo10bo6b2ob2o7b2ob2o$47bob2o2b2obo44b2o2b2ob2o2b2o4b2obobob2o60b2o2b2ob2o2b2o3bo22bo18bo11bo27bo7bo12bo4bo11bo11bo8bo10bo40b2o5b2o9b2ob2o20bo2bo3bo2bo9bo10bo$101bo4bobo4bo8bo64bo4bobo4bo3b2ob2o14b2ob2o19b3o5b3o49b2o2b2o9b2o13b2o5bobo50bo7bo7bo7bo19b3o3b3o$121b3o79bobobo14bobobo21b2o3b2o50bob4obo8b2ob2ob2ob2ob2ob2o5bob2o48bo9bo7bo5bo20b3o3b3o$103bo2bobo2bo10bo66bo2bobo2bo5bo22bo22bo3bo35bo15bo6bo9b4o2bobo2b4o10bo45b2o11b2o4b3o3b3o$104bobobobo9bobobo65bobobobo7bobo16bobo19b3o2bobo2b3o29b2ob2o14bob2obo12bo3bobo3bo9b5o46b3o5b3o7b2o3b2o$104b3ob3o8b7o64b3ob3o9b2o14b2o20bob3o5b3obo28b2ob2o13b3o2b3o12bo7bo12bobo44b2o11b2o$103b2obobob2o7b2obob2o63b2obobob2o5bob2o16b2obo17bobob3ob3obobo27bobobobo12b2o4b2o11bo9bo60bo2bo3bo2bo5bo2bo3bo2bo$106bobo10bobobobo63bob2ob2obo4b2obo18bob2o15b2o4bobobo4b2o26bo5bo30b6ob6o57bo13bo7bobo$105b2ob2o8bo2bobo2bo63bobobobo6bobo18bobo16bo15bo26bo5bo33bobobobo61b2ob2o3b2ob2o5b4ob4o$105bo3bo80bobobobo6b3obo14bob3o17bo13bo28b2ob2o31bob2obobob2obo58b3obo3bob3o8bobo$103b3o3b3o77bo2bobo2bo6bobo16bobo58b2o2bobo2b2o29b2o2bobo2b2o61b2o5b2o5bo2bobobobo2bo$103bo2bobo2bo79b2ob2o8b2o18b2o58b5ob5o31bobobobo64bo5bo5bo3bobobobo3bo$103bo7bo80bobo9bo2bo14bo2bo56b2o4bobo4b2o25b3obobobobob3o58b11o3bobo2bo3bo2bobo$191b2ob2o11bo14bo58bo3b4ob4o3bo97bob7obo6bo7bo$105bo3bo95b3o14b3o56b2ob2o2bobo2b2ob2o23bo6bobo6bo62bo8bo2bo7bo2bo$285b4ob4o27bo2bobobobobobo2bo74bo7bo$207bo14bo62bo7bo27bo3b2obobob2o3bo$206b3o12b3o64b3o35bobobobo77b3o7b3o$205b5o10b5o62b5o36bobo82bo5bo$206b3o12b3o100bo3bobo3bo76bo9bo$206bobo12bobo63bo3bo31b2ob3ob3ob2o$323b2o9b2o75b2ob2ob2ob2o$207bo14bo62b3o3b3o29b2o9b2o74bo4bobo4bo$207b3o10b3o62bo3bo3bo29b2o9b2o73bo2b2obobob2o2bo$209bobo6bobo64bo2b3o2bo29b5o3b5o$207b5o6b5o62b2o5b2o29bo2b3ob3o2bo74bo11bo$207bo14bo64b5o29b2o2b2obobob2o2b2o$208b5o4b5o66bobo30b3ob2o5b2ob3o70b2o13b2o$208b2o2bo4bo2b2o99b2o13b2o71b2o11b2o$212b2o2b2o195b3ob3o$213bo2bo195b2obobob2o$412b2obobob2o$214b2o197b3ob3o$408b3ob2obobob2ob3o$411bob3ob3obo$410bobob2ob2obobo$409b6o3b6o$408bo5bo3bo5bo$408bobo11bobo$409b2o11b2o$410bo2b2o3b2o2bo$409bob2o2bobo2b2obo$409bobo3bobo3bobo$410b4obobob4o$411bobobobobobo$412b2obobob2o$413bobobobo$412b2obobob2o$411b2ob2ob2ob2o$412b2obobob2o$413b3ob3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 2030 HEIGHT 350 ZOOM 4 ]]
(click above to open LifeViewer)


B35678/S4678 (Holstein)

c/2 up to width 14 reports no partial results are found in any symmetry

Velocity Asymmetric Odd-symmetric Even-symmetric
(1,0)c/3 13 < w ≤ 15 19[n 15] 20
15 (JLS)[3]
(1,0)c/4 10 21[n 16] 20
(1,0)c/5 9 15 14
(2,0)c/5 12 23 24
(1,0)c/6 10 19 20[n 17]
(2,0)c/6 10 19 20
(1,0)c/7 9 15 16
(2,0)c/7 10 19 20
(3,0)c/7 11 21 22
(1,0)c/8 7 13 14
(2,0)c/8 8 15 16
(3,0)c/8 11 19 20

notes

  1. non-monotonic!
  2. 9*654 partial
    4b3o$3bob3o$4bo$3bo3b2o$4b2o$6b3o$3b2obo$2bob2obo$2bob2o$5obo$3o3bo$2bob3o$3bob2o$b2ob2o$o2b3o$3b3o$2bobo$bob3o$4b2obo$5b3o$5bobo$o2b4o$b2o2bo$bobo2$2b3o$3bo$2bob3o$5b2o$7bo$5bobo3$3b
    2o$2b4o$5bo$2b2o2bo$2bobo$3b2o$4b2o$3b2obo$3bo3bo$2bobo2bo$2b3obo$4bobo$3bob2o$4bo2$6bobo$5b3o$8bo$2b3ob3o$3b3o$2bo3bo$2b2obo$5bobo$2o2bo2$2b6o$4bob2o$bo$bo$2b3o$5b2o$3b4o$3b2obo$4b3o
    $6bo$4b3o$5bo$2bo$b2o$2b2o$o2b2o2$2obo$2bo2bo$bob3obo$4bobo$5b2o$5bo$6bo$4bo$4bo$2b2o$2b2obo$bo2b2o$b3o$5b3o$2ob2obobo$3o2bobo$2b6o$2b2o2b3o$2bo2bobo$o2b3o2bo$o2b3obo$b5o2bo$obo3bo$4b
    o2bo$3b3o$4b3o$2b3o$bob2o$2bob2o$2bob2o$2bobobo$b2obo$b2o2b2o$b3o$2bo$2bobo$bo3bo$3bo$3b3o$6bo$5b3o$4b2obo$o2bob2o$b2o$2bobo2$bo$2bo$2b3o$2bobo$3b3o$4b2o$5bo$4bo$5b2o$3b4o$2bob4o$3bo2
    b2o$3bobo$3bo$3bob2o$5bo$3b2o$3bobo$5b2o2$6bo2$4bob2o$3bo$4b2o$3bo2bo$2bo2b2o$3b3o$4b2o2$4bo2bo$5b2o$3bo3bo$2b2o$2bo$3bobo$2b4o$2bo2bo$b3obo$bo2bo$3bo2b2o$3bo2bo$4b4o$4bo$5bo$bo2bo$2b
    3o$bo2b2o$bo2bobo$2b4o$b3o$6bo$6bo$5bo$5b2o$5bobo$6b3o$7bo$3b4o$b2o$b2o$2bob2o$2bo$o$2o2$2b2o$2bo$3b5o$6bo$6bo$2bo3bo$b2obo$bobobo$2b2obo2$b2obo$4bo$3bo$bo2b2o$3b2o2bo$3b2obo$3bo2$2b2
    o$3bo$3bo$b2o$b2o$2bobo2$5b3o$7bo$4b2o$4bo$4bobo2$2b2o3b2o$2bob4o$4bo$4b2o$bo$3o$o2b2o$3bo$bo2$2b3o$3b2o$2bo$2bobo$4bo2$3b2o$3b3o$3bob2o$3bo$4b2o$3b3o$3b3o$2bob2o$5b2o$b3o$b4o$7bo$5bo
    b2o$b2o3b3o$obo$obo2bo2bo$7bo$7bo2$5b2o2$6bo$4bo$2b3o$2bobo$2bo4bo$3bo2b2o$3bo$3bo$6bo$5bo$2b3o$2bobob2o$bob2obo$2obob2o$2o3bo$5bo$2b4o$2bob3o$2bo$4bo$2bo$4bobo$bobobo$4b3o$4bo2bo$3b5
    o$4bobo$4b2o$5b2o$4b2o$4bo$6bo$3b2o2bo$4b2obo$5o$3bo2bo$4obo$2b4o$bo$3bobo$4b2o$3b3o$3bo3bo$6b2o$6bo$4bo$2b3o$b3o$3bobo$5bo$7bo$5b2o$3b3obo$5b2o$2bobo$2b2o2bo$4bo2$3bobo$5b2o$4b2o$4b3
    o$4b2o$4bo2$2bobo$3b2o$b2o$2o2bob2o$o2b2o2bo$bo3bo$6bo$7b2o2$5b3o2$3b2o$2bo$2b3o$3b2obo$3bobo3$3b2o$3b2o2bo$3bo2b3o$2bob3obo$4bo$3b2o$b3o$2b3o3$2b3o$2b3o$2bo3bo$2bobobo$3b2o$bob2o$obo
    $4bobo$2bo$3b4o$3b2obo2$4b2o$3bo2bo$4bob2o$4bobo$3b2ob2o$4bob2o$4b2obo$4bo$4bobo$3b3obo$4b3o$3bo$5b2o$4b3o$4bo$bo2b2o$2o4bo$b4o$obo2bo$b2o$2bo3b2o$2b5o$2b2o3bo$5b2o$5bo$7bo$5b2o$5bo$5
    bobo$4bob2o$3b3obo$2b3obo$2bob2obo$bob2ob2o$2b4obo$6bo$3bo$4bo$4b2obo$5bobo2$4bobo$5b2o2$4b2o$4bo$3b2o$4bo2$4b2o$3b3obo$3bo2b2o$3bobo$3bobobo$4bo2bo$4bo2bo$5b2o$3b2o2b2o$4b2o2bo$4bob2
    o$5b3o$5b3o$5b2o$6bobo$3b2ob2o2$6b2o$5b4o$6b2o$5b3o$3b2obo$b3obo$b4o$2b2o2bo$2bo$bo4bo$4b3o3$3b3o2$3bo$2b2o$b2obo$bo2bobo$2b3obo2$2bob3o$4b2o$5b2o3$2bo$2ob2o$bobo$o3bo$bobo$3bo$2bobo$
    2b4o$3b5o$3bo3b2o$5bobo$6bobo$6bo$3b2o$3bobo$2b3obo$4b2obo$b4ob2o2$4bo$2bob3o$2b6o$2b2obobo$3b3ob2o$3b2o2bo$2bo4bo$2b2o$bo2b2o$2b2obo$bo2$2bo$2b4o$bo3bo$4b2o$4b3o$5b2o$5b2o$6bo$2bob2o
    $3b2obo$3bob2o$3b2o$3b2o$2b2o$3bo$2bobo$bo$2b2o$3bo$bo$2bo$2b4o$2bo2bo$b2ob2o$bo2bo$3o2b2o$bobo$bo2b3o$b4o$ob3o$3o2b2o$b2ob2o$2b2o2bo$2b2o$2ob3o$2bob2o$2bob2o$3b4o$4bo$2b3o2$2b4o$3bo$
    3bob3o$3b2o3bo$5bobo$6bo$3b2o2bo$2bobo$3bo2$4b2o$3b2o$3b2o$3bo$bo2bo$bo2bo$3o$bo$ob4o$4b2o$b3obo$3b2o$2bob2o$3b3o$2bo3bo$2b4o$4b3o$bo$o2bo$ob2o$4b2o$5bo$2b2o$5b3o$4bo2bo$3b4o$bo2bo$b3
    o$2o2b2o$2o2bo$3bo2bo$b2obo$o2bo$5b2o$6b2o$2b4o$3bobo$4bo$3bo$5bo$5b2o$5b2o$5bob2o$7b2o$6bo$6bo2$3bob2o$3bo3bo$5o2b2o$bo2b2o$o2bobo$2b3o$3bo3bo$3bobo$3b2o$3b2obo2$b4obo$b2obo$3bo$3bo$
    4bobo$4b2ob2o2$3b3obo$3bob3o$5b2o$4b3o$4b3o$3b2ob2o$6bo$4b3o$5bo$3b3o$3b3obo$4b3obo$4bobo$2bob3o$3bobo$3b4o$2bob2o$2b6o$2b2o2bo$7b2o$3bo3bo$2bob2obo$3bob2obo$3b2ob3o$5b2o$4b2o$2b2o$3b
    ob2o$3o2b2o$b4ob2o$2obob2o$2b2o$2bo2bo$5o$bob5o$bob5o$bobobo$ob4o$4bobo$b5o$b2o2bo$3bobobo$5bobo$4bob2o$2bobobo$2b2o$2b2o$bo4b2o$4b2o2bo$3b5o$2b2obobo$2bobo2b2o$o5b3o$3b2obo$2ob2o2bo!
  3. found by the dreamweaver, who specified that it is not guaranteedly minimal-length for a width-11 since the search split and only one branch was necessary to search to find it, but shows that 11 is the minimum
    shares frontend with the longest width-10 (10*65) partial
    5bobo$5b3o$4bob2o$2b4o2bo$2b4o$6bobo$9bo$5bobo$4b4o$3bobobo$3b2o$5bobo$5b4o$4bobo$4b2obobo$4b2o$4b5o$3b2o$4bo3bo$2b2ob4o$2bobob2o$3bobobo$3b2o$2b2
    obo$b2o2b2o$7bo$3bo$2bo3b3o$2bob2obobo$2bobobob2o$4b2o2bo$6b4o$4b2obo$4b3o$5b2o2$3b2obo$2bo3b3o$3b2obobo$3b2obobo$3b2obobo$o2b5o$7b2o$2b3o2bo$2bo4
    bo$3bo3bo$3b2o2b2o$2bo2b3obo$b2obo$b2obo$o4bo$b2ob2o$3b5o$b4obo$bo2bo2bo$9o$bob4obo$2bo2bo2b2o$2bo2bobo$5bo3bo$2bobo$bobo$b3o2b4o$2obobob2o$3b4obo!
  4. this spaceship (with a forked tail) is in fact shorter, but higher-population
  5. 10*30 partial
    5b2o$4b3o$7b2o$4b3obo$4bo3bo$5b3o$7bo$6bo$3bo3b2o$3b2o$3b6o$4bobob2o$5b5o$4bo$5bo$3b5o$2bobo3bo$5b2
    o2bo$b2o2bo$2b2o2bo$obobo$3obobo$b2obob2o$o2b6o$b2ob2o2b2o$2bo4b2o$bob3ob2o$2b2o3bobo$3b3o3bo$ob2o!
  6. 19*86 partial
    b4o9b4o$2b2o11b2o$2bobo9bobo$b5o7b5o$4bo9bo$b2o13b2o$bobo11bobo$2bob2o7b2obo$3b
    obo2b3o2bobo$3b3o7b3o$3b2o9b2o$3bob2o5b2obo$8b3o$9bo$7bobobo$5b2o2bo2b2o$5bo2b3
    o2bo$4bo2bo3bo2bo$4bob2o3b2obo$3bob2ob3ob2obo$6b7o$8bobo$3bo2bob3obo2bo$3b4obob
    ob4o$4b3o5b3o$4b2ob2ob2ob2o$6b2o3b2o$6b2o3b2o$6b3ob3o$5bobo3bobo$4bo2b5o2bo$4b2
    o7b2o$3b3o7b3o$4b5ob5o$6bob3obo$4bo2bobobo2bo$4b2obobobob2o$3bobo2b3o2bobo$4b4o
    bob4o$4b2obo3bob2o$3b2o2bo3bo2b2o$3bob3o3b3obo$4b2o7b2o$4b2ob2ob2ob2o$6b2o3b2o$
    4b2o2bobo2b2o$4bo9bo$4bobo5bobo$5b2o5b2o$3b3o2bobo2b3o$2bo2b2o5b2o2bo$3bo3bo3bo
    3bo$2o3bo7bo3b2o$bo3b2o5b2o3bo$2ob3o7b3ob2o$bob3o3bo3b3obo$b3obobobobobob3o$2bo
    4bobobo4bo$2b4o3bo3b4o$2b3o9b3o$4b5ob5o$2b2o3bo3bo3b2o$2bo2b4ob4o2bo$bobob2obob
    ob2obobo$3bobob5obobo$bobo2bobobobo2bobo$o2bobo2bobo2bobo2bo$b2o2bo3bo3bo2b2o$2
    o4bobobobo4b2o$ob2o2b2obob2o2b2obo$6b7o$4b3o5b3o$4b2o7b2o$4b5ob5o$2bo3bobobobo3
    bo$4bo2b5o2bo$b4obo5bob4o$4bo2bobobo2bo$bo3bobo3bobo3bo$b2obobob3obobob2o$b2obo
    b3ob3obob2o$b2o2b3o3b3o2b2o$2bob2o3bo3b2obo$4b2o2b3o2b2o$b3o11b3o$3bo3bo3bo3bo!
  7. 19*33 partial
    7b5o$5bobobobobo$5b3obob3o$4bo2b2ob2o2bo$2bo2b9o2bo$2bo6bo6bo$2bob4o3b4obo$5b3obob3o$5bo2bobo2bo$3bo3b5o3bo$2b2o2bo2bo2bo2b2o$3bob2o2bo2b2obo$3b6ob6o$7bo3bo$8bobo$2bo2bobo3bobo2bo$2b2o3b5o3b2o$3b3obo
    3bob3o$2bo6bo6bo$3bo2bo2bo2bo2bo$b3o2bo2bo2bo2b3o$3bo2bobobobo2bo2$b2ob4obob4ob2o$b2o3b7o3b2o$3b6ob6o$2bo5bobo5bo$5bo2b3o2bo$b2obo2b5o2bob2o$5bo2b3o2bo$2o4bob3obo4b2o$3o2b2o5b2o2b3o$b2obo3bobo3bob2o!
  8. 20*39 partial
    5bo2b4o2bo$4b2ob6ob2o$3b2obo6bob2o$3b5ob2ob5o$3bo2b2ob2ob2o2bo$6b2o4b2o$4b2ob2o2b2ob2o$4b2ob2o2b2ob2o$3b2ob2ob2ob2ob2o$2b
    ob2obob2obob2obo$2b3obo6bob3o$3b5o4b5o$5b4o2b4o$2b5obo2bob5o$bobo2b2o4b2o2bobo$2bo2bo8bo2bo$bobo12bobo$2b3o10b3o$2b3o10b3
    o$3b3o8b3o$2bob2obo4bob2obo$b3obob2o2b2obob3o$bo5bo4bo5bo$2o4bo6bo4b2o$4o3bo4bo3b4o2$b3o3bob2obo3b3o$3bo2b8o2bo$b2o5b4o5b
    2o$5b3o4b3o$o6b6o6bo2$b3o2b2o4b2o2b3o$3bob3o4b3obo$7bob2obo$2b2o3b2o2b2o3b2o$2obobob2o2b2obobob2o$b2ob12ob2o$b3o5b2o5b3o!
  9. 12*70 partial
    5b2o$4b4o$5b2o$4bo2bo$4bo2bo$3b6o$2b2o4b2o$3b6o$3b2o2b2o$3b6o$4b4o2$4b4o$4bo2bo$5b2o$3b6o$4bo2bo$4bo2bo$4b4o$4bo2bo$4bo2bo$5b2o$4b
    4o$4b4o$bobo4bobo$3bo4bo$b3o4b3o$2b2o4b2o$b2o6b2o$ob3o2b3obo$b2o2b2o2b2o$12o$2b8o$3b6o2$2b2o4b2o$bobo4bobo$2ob2o2b2ob2o$bo2bo2bo2b
    o$b3o4b3o$b2obo2bob2o$3b2o2b2o$3bob2obo$2bo2b2o2bo$5b2o$2b8o$4bo2bo$5b2o$b2obo2bob2o$2bo6bo$3bob2obo$3bo4bo$2bo2b2o2bo$4bo2bo2$3b2
    o2b2o$3bob2obo$5b2o2$2b8o$bo3b2o3bo$bo3b2o3bo$bo2bo2bo2bo$2bo2b2o2bo$2bo2b2o2bo$b4o2b4o$b2obo2bob2o$b2obo2bob2o$2bob4obo$3bob2obo!
  10. 12*48 partial
    4b4o$2b8o$4b4o$b2obo2bob2o$3bo4bo$3bob2obo$2b2o4b2o$2b2o4b2o$3b2o2b2o$4bo2bo$3b6o$5b2o$2bo6bo$2o8b2o$bobo4bobo2$3b2o2b2o$b2o6b2o$2bo6bo$3bo4bo$bo3b2o3bo2$2o8b2o$12o$b10o$2b2o4b2o$
    3bo4bo$4b4o$4bo2bo$2b2ob2ob2o$2bo6bo$3bob2obo$ob2o4b2obo$ob3o2b3obo$b10o$2bo2b2o2bo$2obob2obob2o$b4o2b4o$bob6obo$5b2o$bo8bo$3bob2obo$2b2o4b2o$5o2b5o$4o4b4o$bo3b2o3bo$3b6o$b2o6b2o!

    and 14*54
    6b2o$4b2o2b2o$3b8o$3bobo2bobo$3b2o4b2o$4b6o$4b6o$4b2o2b2o$4b2o2b2o$5b4o$5b4o$4bo4bo$2b3o4b3o$2b2o6b2o$2b3o4b3o$3b2o4b2o$3b3o2b3o2$3bo6bo$b2obo4bob2o$b4o4b4o$2ob2o
    4b2ob2o$2b3o4b3o$2bo2b4o2bo$3bo2b2o2bo$2bo2bo2bo2bo$4b6o$bo4b2o4bo$5bo2bo$3b3o2b3o$4b2o2b2o$4bo4bo$2bo2bo2bo2bo$2bo2bo2bo2bo$2bo2bo2bo2bo$2b2obo2bob2o$5b4o$3bo6bo
    $4b2o2b2o$2b2obo2bob2o$bobob4obobo$bo4b2o4bo$b5o2b5o$4bob2obo$3b2ob2ob2o$2b3o4b3o$3b3o2b3o$2ob8ob2o$o3b2o2b2o3bo$2bob2o2b2obo$2bo2b4o2bo$3bo2b2o2bo$o12bo$bob8obo!

    seems promising
  11. 19*47 partial
    2b15o$b4o4bo4b4o$5b2obobob2o$b2obob2o3b2obob2o$2b2o2b2o3b2o2b2o$bo4b3ob3o4bo$4bobob3obobo$6bob3obo$bobo2b3ob3o2bobo$b3obo2bobo2bob3o$b2o2bobo3bobo2b2o$3bob
    2o5b2obo$6b3ob3o$5bobo3bobo$2bo2bo2bobo2bo2bo$bo2bobo5bobo2bo$b2ob2o7b2ob2o$b4ob7ob4o$bob2obob3obob2obo$2bo6bo6bo$b2ob11ob2o$bo2bo9bo2bo$3b2ob7ob2o$b3o2b2o
    3b2o2b3o$bo2bobo5bobo2bo$b2o2bobo3bobo2b2o$b2o5bobo5b2o$3bo2bobobobo2bo$bob5o3b5obo$7bo3bo$2o4bo5bo4b2o$b3o11b3o$bo3bob2ob2obo3bo$bob2o2bo3bo2b2obo$2bo3bo5b
    o3bo$b3obo7bob3o$b3o11b3o$2bo4bo3bo4bo$7ob3ob7o$bob4o5b4obo$2ob5o3b5ob2o$5bobo3bobo$3b2o3bobo3b2o$3b3o2bobo2b3o$3bob2o2bo2b2obo$3b3o2bobo2b3o$3o3b3ob3o3b3o!
  12. 20*30 partial
    8b4o$6b8o$5b3o4b3o$8bo2bo$3bo3bob2obo3bo$4b2o2bo2bo2b2o$2b2o2bo2b2o2bo2b2o$2b2ob2obo2bob2ob
    2o$3bob10obo$3bo3bo4bo3bo$3bobo2bo2bo2bobo$5bo8bo$5b3ob2ob3o$5b4o2b4o$5bobo4bobo$7b6o$6bo6b
    o$2b3ob3o2b3ob3o$4bob2ob2ob2obo$b3ob3ob2ob3ob3o$bob3o8b3obo$2b2o2b2o4b2o2b2o$5b2o6b2o$3bobo
    bo4bobobo$b3obobob2obobob3o$bo2bo3bo2bo3bo2bo$o5bobo2bobo5bo2$ob3obo6bob3obo$bo4b3o2b3o4bo!
  13. 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 though preceding width has been disproven, this was not found with qfind so is not guaranteed to be of minimal height
  14. 14.0 14.1 unique thinnest
  15. this one has a smaller population but a backspark that increases its bounding box
  16. not sure of minimality of length
  17. 20*46 partial
    7b6o$5bob2o2b2obo$3bobob6obobo$bob3ob6ob3obo$bob14obo$ob4obob2obob4obo$b5ob6ob5o$b18o$b4obo6bob4o$3b3o8b3o$bobobo8bobobo$bob3o8b3obo$2b2o5b2o5b2o
    $ob5o2b2o2b5obo$obobobobo2bobobobobo$2bobobob4obobobo$4bob8obo$2b5ob4ob5o$2bobob2o4b2obobo$3b5ob2ob5o$2b5o6b5o$2bob4o4b4obo$4b2o8b2o$2b3obobo2bo
    bob3o$3b4o2b2o2b4o$b8o2b8o$4bobob4obobo$3b4ob4ob4o$bob2obob4obob2obo$bob14obo$bob5o4b5obo$4b4o4b4o$b7o4b7o$4bo2b2o2b2o2bo$2b3obo6bob3o$4bobo6bob
    o$2b2o12b2o$2b16o$2bobo2b2o2b2o2bobo$2bo2bobob2obobo2bo$4b2ob6ob2o$b2o3b3o2b3o3b2o$2b4o3b2o3b4o$4o2bo2b2o2bo2b4o$ob3ob8ob3obo$2bobob2ob2ob2obobo!

other such tables alike this

references

  1. LaundryPizza03 (March 25, 2024). Re:B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
  2. wwei47 (April 27, 2024). Re:RLE copy/paste thread - everyone else (discussion thread) at the ConwayLife.com forums
  3. wwei47 (April 25, 2024). Re:RLE copy/paste thread - everyone else (discussion thread) at the ConwayLife.com forums