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
(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
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#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 WIDTH 3360 HEIGHT 1085 ZOOM 4 ]]
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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
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)
29 (JLS)
28 (JLS)
29 (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
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
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
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
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 ]]
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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
↑ non-monotonic!
↑ 9*654 partial4b3o$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!
↑ 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 ) partial5bobo$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!
↑ this spaceship (with a forked tail) is in fact shorter, but higher-population
↑ 10*30 partial5b2o$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!
↑ 19*86 partialb4o9b4o$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!
↑ 19*33 partial7b5o$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!
↑ 20*39 partial5bo2b4o2bo$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!
↑ 12*70 partial5b2o$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!
↑ 12*48 partial4b4o$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$bob8obo! seems promising
↑ 19*47 partial2b15o$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!
↑ 20*30 partial8b4o$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!
↑ 13.0 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
↑ 14.0 14.1 unique thinnest
↑ this one has a smaller population but a backspark that increases its bounding box
↑ not sure of minimality of length
↑ 20*46 partial7b6o$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