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[[512,18,18]] d ≤
n
512
k
18
d
18
kd²/n
11.391
w
8
X/Z
1.11
g
0.0352
r
4.2426
layers
2
swaps
1677

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Distance

X/Z asymmetry 1.11 · d_X ≤ 20, d_Z ≤ 18 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 20 · witness weight 20 (claimed upper_bound)
witness found by @MathysRennela · research/kit/surrogate.lightest_logical · found at 5×104 trials · survived 5×104 trials · 2026-10-10
witness operator (support, 20 qubits)
[199, 216, 229, 248, 268, 279, 302, 313, 327, 330, 333, 347, 364, 375, 395, 409, 423, 426, 457, 471]
d_Z 18 · witness weight 18 (claimed upper_bound)
witness found by @MathysRennela · research/kit/surrogate.lightest_logical · found at 5×104 trials · survived 5×104 trials · 2026-10-10
witness operator (support, 18 qubits)
[95, 140, 154, 168, 174, 182, 185, 196, 202, 213, 219, 241, 244, 247, 250, 253, 450, 480]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–8 (mean 6.8) · H_Z 3–8 (mean 6.737)
qubit degrees H_X 1–6 (mean 3.453) · H_Z 1–4 (mean 3.25)
trapping sets H_X (1,1)×45 (2,1)×108 (3,0)×39 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 45 (1,2): 88 (1,3): 51 (1,4): 256 (1,5): 62 (1,6): 10 (2,1): 108 (2,2): 133 (2,3): 350 (2,4): 639 (2,5): 506 (2,6): 2730 (2,7): 528 (2,8): 245 (2,9): 108 (2,10): 9 (3,0): 39 (3,1): 127 (3,2): 406 (3,3): 1587 (3,4): 2649 (3,5): 5440 (3,6): 11478 (3,7): 9811 (3,8): 40559 (3,9): 9587 (3,10): 8736 (3,11): 2859 (3,12): 1598 (3,13): 359 (3,14): 36
trapping sets H_Z (1,1)×48 (2,0)×13 (3,0)×13 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 48 (1,2): 96 (1,3): 48 (1,4): 320 (2,0): 13 (2,1): 102 (2,2): 199 (2,3): 330 (2,4): 668 (2,5): 522 (2,6): 3405 (3,0): 13 (3,1): 177 (3,2): 586 (3,3): 1458 (3,4): 3078 (3,5): 5766 (3,6): 12682 (3,7): 9632 (3,8): 51785 (3,9): 845 (3,10): 5852
witness diameter X 15.6525 · Z 17.4929 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4.243
X checkZ checkqubit site (256)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 1677 nearest-neighbor SWAPs per round in total, at most 4 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction Open-boundary weight-8 planar tile code (bivariate bicycle) on a 16x16 lattice via research/local2d/boundary_engine.build_planar: A-support f={(0,0),(0,3),(2,2),(3,0)}, B-support g={(0,2),(1,3),(2,0),(3,3)} (two supports, second-order boundary generators completed by exact half-infinite boundary gauge operators over F2[t] with corner topological-order completion). The same call at (21,22) reproduces the board's codes/924-18-31.json check-for-check, which calibrates the generator. Layout is the square-grid coordinate map planar.grid_coordinates(16,16) with 2 qubits per site, layers=2. This B-support is NOT the arXiv:2504.09171 B=4 weight-8 tile; see provenance.notes.
model Space Bunny Alpha 1.0 (claimed, not verified)
builds on arXiv:2504.09171, arXiv:2504.08887, arXiv:2410.11942
date 2026-10-10
notes Independent construction at the published geometry, not the published code. The same generator call at (21,22) reproduces the board's codes/924-18-31.json check-for-check, so the generator itself is calibrated rather than inferred. CORRECTION (2026-10-10): an earlier revision of this entry named itself [[512,18,19]] and read its d<=18 as a failure to reproduce the paper's exact d=19. That was wrong, and the error was in the identification, not the distance. arXiv:2504.09171 carries its B=4 weight-8 tile in the LaTeX source as literal \def macros (main.tex lines 690-691, repeated at 763-764): X-tile horizontal edges {(0,0),(0,3),(2,2),(3,0)} and vertical edges {(0,1),(1,0),(1,1),(3,3)}. This entry's A-support matches the published horizontal edges exactly, but its B-support differs from the published vertical edges in three of four monomials. Rebuilt with the published tile, this repo's generator reproduces the paper's two exact distances at the two sizes the paper publishes: d<=13 at a 12x12 lattice (9x9 bulk tiles, the paper's [[288,18,13]]) and d<=19 at this 16x16 lattice (13x13 bulk tiles, the paper's [[512,18,19]]). The B-support used here instead gives d<=11 and d<=18 at those same two sizes. So the weight-18 Z-logical stored in this entry is a true statement about a different code, and it does not refute, and is not in tension with, the published [[512,18,19]] -- which stands. A sibling B-support, g={(0,1),(1,1),(2,0),(3,3)}, recorded by the board's codes/566-18-20 and codes/578-18-20 and differing from the published tile in the single monomial (1,0) vs (2,0), gives d<=11 at 12x12 and is likewise not the published code; no claim is made about it. The distance here is an upper bound from an explicit witness, not an exact claim; exact certification is the maintainer-side verify/certify.py tier and is not asserted. On the Pareto frontier this entry is additive rather than displacing: nothing on the board is dominated by it, and it does not lead its cell on kd^2/n (11.39, against [[184,50,10]] at 27.17 and [[192,20,16]] at 26.67 on the CSS weight-8 2D-local bilayer cell; [[155,6,23]] at 20.48 is a stabilizer-board entry and does not compete in a CSS cell). It adds a new nondominated point at n=512, k=18, which is below every existing k=18 tile entry (n=562, n=563, n=924).
family tile (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[512,18,18]] The 16x16 member of the board's weight-8 planar tile family, d <= 18 by explicit witness, one below the published [[512,18,19]] but a DIFFERENT CODE from it

Correction (2026-10-10)

An earlier revision of this note and of codes/512-18-18.json read the d <= 18 below as a failure to reproduce the published exact d = 19 of [[512,18,19]] (arXiv:2504.09171), and the entry's name field carried [[512,18,19]]. That was an identification error, not a distance error, and the distance is unaffected: the stored weight-18 Z-logical is a genuine logical of the code in the diff, and verify/qldpc_verify.py still accepts the file.

arXiv:2504.09171 specifies its B=4 weight-8 tile in the LaTeX source as literal \def macros (main.tex lines 690-691, repeated at 763-764), not only in a figure: X-tile horizontal edges {(0,0),(0,3),(2,2),(3,0)}, vertical edges {(0,1),(1,0),(1,1),(3,3)}. This entry's A-support is the published horizontal set exactly; its B-support {(0,2),(1,3),(2,0),(3,3)} differs from the published vertical set in three of four monomials.

Rebuilt with the published tile, build_planar reproduces the paper's two published exact distances at both sizes the paper gives them: d <= 13 at a 12x12 lattice (9x9 bulk tiles, the paper's [[288,18,13]]) and d <= 19 at 16x16 (13x13 bulk tiles, the paper's [[512,18,19]]). The B-support used by this entry gives d <= 11 and d <= 18 at those same two sizes. Both readings were checked with verify/qldpc_verify.py's own gf2.commutes / gf2.in_rowspace, not only through the kit's surrogate.

So this entry is the board's own construction at the published geometry. The published [[512,18,19]] stands, unreproduced and un-refuted; it is simply a different code. research/local2d/boundary_engine.py carried the mislabelling and is being corrected separately; the published B-support is the value above, which that module does not currently export.

Direction & hypothesis

Aimed at the weight-8 x local-2d-bilayer cell, which is where the board's own tile family lives and where the frontier was thinnest in the k=18 strand. TRACKS.md names [[512,18,19]] (arXiv:2504.09171) as the published weight-8 2D-local bar and it was never seeded: the family was on the board at n=924 (d=31) and n=566/563/562 (d=19..20), but at nothing below n=562. The opening was therefore not a new construction but a lattice size the family had never been built at, combined with an honest re-measurement of the distance rather than an inherited one.

What was searched

The open-boundary planar tile builder research/local2d/boundary_engine.build_planar over lattice sizes 12x13 through 21x22, on two B-supports: S_G_TILE4_MAIN={(0,2),(1,3),(2,0),(3,3)} and the sibling g={(0,1),(1,1),(2,0),(3,3)} that the board's codes/566-18-20 records for this family. The generator was calibrated first, by check-matrix comparison rather than by (n,k,w), as research/AUTORESEARCH.md section 3 requires: the call at (21,22) reproduces codes/924-18-31.json with all 475 X rows and all 450 Z rows identical. Screening was the kit surrogate, per side, plus an independent threaded gf2_fast pass used to try to break the claim rather than to support it.

Evidence trail

Confirmation ladder for the submitted code, each rung a fresh seed unless marked otherwise, reading the lightest logical found:

| budget (trials/side) | lightest logical | | ---: | ---: | | 50,000 (RIS per side, seed 20261010, via submit.make_submission (dX=20, dZ=18)) | 18 | | 1,000,000 (gf2_fast, 2,000,000 accelerator trials shared across the two sides (1,000,000 per side), seed 11) | 18 |

2 fresh-seed rung(s) agree at the best bound, the deepest of them at 1,000,000 trials per side. The submitted witness reproduces it: X: d <= 20 (upper_bound), Z: d <= 18 (upper_bound).

Both rungs are fresh seeds and both settle at 18, so the bound is 2 flat fresh rungs deep at the minimum rung count research/kit/escalation.py requires. The second rung is an independent mechanism from the first - the accelerator rather than the NumPy RIS path - which is why it counts as corroboration and not repetition. The per-side figure is what promote.py compares against, since its own reference point is the CLI's 2,000,000 accelerator trials shared across two sides.

Dead ends

  • A 20,000-trial RIS probe read d=19 and that reading was carried into an

    • early draft. A 50,000-trial packaging search and an independent 2,000,000-trial accelerator search both went lower, to 18, so the probe was the soft measurement rather than the code being unusually good. The early kd^2/n estimate of 12.69 was computed from that probe and is wrong; at d=18 the figure is 11.39.

  • This is the failure the board's own note on notes/562-18-19.md records: a

    • distance read at one budget is not a distance. The 20,000-trial reading of 19 was soft, and the entry claims d <= 18 from its own witness with no exactness asserted. What that re-measurement does NOT do is undercut the published d = 19: the code measured here is not the published code, which is the correction above.

  • Left open, and now settled by the correction above: the sibling B-support

    • also gives n=512, k=18, w=8 at this lattice size, and an earlier revision left open which of the two codes the published [[512,18,19]] denotes. It is neither. The published tile is a third support pair, g={(0,1),(1,0),(1,1),(3,3)}, recovered from the paper's own source rather than from any board entry. No claim is made about the sibling.

Tools

Model: Space Bunny Alpha 1.0 (opencode). Repo tooling: research/kit/submit.py, research/kit/surrogate.py, research/kit/coordination.py, research/kit/promote.py, research/local2d/boundary_engine.py, research/local2d/planar.py, verify/gf2_fast. The local verdict is verify/validate_candidate.py; the bundle was assembled by research/kit/promote.py. Compute: CPU only, 8 cores, no GPU present. The packaging search spent 3,562s for 50,000 trials per side; the accelerator pass spent 337s for 2,000,000 shared trials at 4 threads.

Reproduction

research/local2d/boundary_engine.build_planar(16, 16, S_F_TILE4, S_G_TILE4_MAIN), with S_F_TILE4=((0,0),(0,3),(2,2),(3,0)) and S_G_TILE4_MAIN=((0,2),(1,3),(2,0),(3,3)), both module constants of research/local2d/boundary_engine.py. This yields n=512, k=18, check weight 8. The layout is research/local2d/planar.grid_coordinates(16, 16, kept=info['kept_qubits']) with layers=2, giving 512 coordinates, 256 distinct sites, 2 qubits per site and interaction radius 4.2426 = 3*sqrt(2), which is over the 4.0 single-layer cap and inside the 7.0 bilayer cap. The same call at (21,22) reproduces codes/924-18-31.json check-for-check, so the calibration is reproducible from committed code.

To reproduce the identification in the correction section instead, call the same builder with the published B-support spelled out literally: build_planar(16, 16, S_F_TILE4, ((0,1),(1,0),(1,1),(3,3))) gives d <= 19 at 16x16 and, at 12x12, d <= 13. Note that this build emits redundant stabilizers of weight 12-18 on the Z side; all of them lie in the row space of the weight-8 rows (rank 247 either way), so dropping the rows of weight > 8 recovers the paper's weight-8 stabilizer set.

Parity checks

X-checks 260 (max weight 8) · Z-checks 247 (max weight 8)
H_X (260 checks, sparse supports)
[0, 3, 34, 48, 258, 275, 288, 307] [1, 4, 35, 49, 259, 276, 289, 308] [2, 5, 36, 50, 260, 277, 290, 309] [3, 6, 37, 51, 261, 278, 291, 310] [4, 7, 38, 52, 262, 279, 292, 311] [5, 8, 39, 53, 263, 280, 293, 312] [6, 9, 40, 54, 264, 281, 294, 313] [7, 10, 41, 55, 265, 282, 295, 314] [8, 11, 42, 56, 266, 283, 296, 315] [9, 12, 43, 57, 267, 284, 297, 316] [10, 13, 44, 58, 268, 285, 298, 317] [11, 14, 45, 59, 269, 286, 299, 318] [12, 15, 46, 60, 270, 287, 300, 319] [16, 19, 50, 64, 274, 291, 304, 323] [17, 20, 51, 65, 275, 292, 305, 324] [18, 21, 52, 66, 276, 293, 306, 325] [19, 22, 53, 67, 277, 294, 307, 326] [20, 23, 54, 68, 278, 295, 308, 327] [21, 24, 55, 69, 279, 296, 309, 328] [22, 25, 56, 70, 280, 297, 310, 329] [23, 26, 57, 71, 281, 298, 311, 330] [24, 27, 58, 72, 282, 299, 312, 331] [25, 28, 59, 73, 283, 300, 313, 332] [26, 29, 60, 74, 284, 301, 314, 333] [27, 30, 61, 75, 285, 302, 315, 334] [28, 31, 62, 76, 286, 303, 316, 335] [32, 35, 66, 80, 290, 307, 320, 339] [33, 36, 67, 81, 291, 308, 321, 340] [34, 37, 68, 82, 292, 309, 322, 341] [35, 38, 69, 83, 293, 310, 323, 342] [36, 39, 70, 84, 294, 311, 324, 343] [37, 40, 71, 85, 295, 312, 325, 344] [38, 41, 72, 86, 296, 313, 326, 345] [39, 42, 73, 87, 297, 314, 327, 346] [40, 43, 74, 88, 298, 315, 328, 347] [41, 44, 75, 89, 299, 316, 329, 348] [42, 45, 76, 90, 300, 317, 330, 349] [43, 46, 77, 91, 301, 318, 331, 350] [44, 47, 78, 92, 302, 319, 332, 351] [48, 51, 82, 96, 306, 323, 336, 355] [49, 52, 83, 97, 307, 324, 337, 356] [50, 53, 84, 98, 308, 325, 338, 357] [51, 54, 85, 99, 309, 326, 339, 358] [52, 55, 86, 100, 310, 327, 340, 359] [53, 56, 87, 101, 311, 328, 341, 360] [54, 57, 88, 102, 312, 329, 342, 361] [55, 58, 89, 103, 313, 330, 343, 362] [56, 59, 90, 104, 314, 331, 344, 363] [57, 60, 91, 105, 315, 332, 345, 364] [58, 61, 92, 106, 316, 333, 346, 365] [59, 62, 93, 107, 317, 334, 347, 366] [60, 63, 94, 108, 318, 335, 348, 367] [64, 67, 98, 112, 322, 339, 352, 371] [65, 68, 99, 113, 323, 340, 353, 372] [66, 69, 100, 114, 324, 341, 354, 373] [67, 70, 101, 115, 325, 342, 355, 374] [68, 71, 102, 116, 326, 343, 356, 375] [69, 72, 103, 117, 327, 344, 357, 376] [70, 73, 104, 118, 328, 345, 358, 377] [71, 74, 105, 119, 329, 346, 359, 378] [72, 75, 106, 120, 330, 347, 360, 379] [73, 76, 107, 121, 331, 348, 361, 380] [74, 77, 108, 122, 332, 349, 362, 381] [75, 78, 109, 123, 333, 350, 363, 382] [76, 79, 110, 124, 334, 351, 364, 383] [80, 83, 114, 128, 338, 355, 368, 387] [81, 84, 115, 129, 339, 356, 369, 388] [82, 85, 116, 130, 340, 357, 370, 389] [83, 86, 117, 131, 341, 358, 371, 390] [84, 87, 118, 132, 342, 359, 372, 391] [85, 88, 119, 133, 343, 360, 373, 392] [86, 89, 120, 134, 344, 361, 374, 393] [87, 90, 121, 135, 345, 362, 375, 394] [88, 91, 122, 136, 346, 363, 376, 395] [89, 92, 123, 137, 347, 364, 377, 396] [90, 93, 124, 138, 348, 365, 378, 397] [91, 94, 125, 139, 349, 366, 379, 398] [92, 95, 126, 140, 350, 367, 380, 399] [96, 99, 130, 144, 354, 371, 384, 403] [97, 100, 131, 145, 355, 372, 385, 404] [98, 101, 132, 146, 356, 373, 386, 405] [99, 102, 133, 147, 357, 374, 387, 406] [100, 103, 134, 148, 358, 375, 388, 407] [101, 104, 135, 149, 359, 376, 389, 408] [102, 105, 136, 150, 360, 377, 390, 409] [103, 106, 137, 151, 361, 378, 391, 410] [104, 107, 138, 152, 362, 379, 392, 411] [105, 108, 139, 153, 363, 380, 393, 412] [106, 109, 140, 154, 364, 381, 394, 413] [107, 110, 141, 155, 365, 382, 395, 414] [108, 111, 142, 156, 366, 383, 396, 415] [112, 115, 146, 160, 370, 387, 400, 419] [113, 116, 147, 161, 371, 388, 401, 420] [114, 117, 148, 162, 372, 389, 402, 421] [115, 118, 149, 163, 373, 390, 403, 422] [116, 119, 150, 164, 374, 391, 404, 423] [117, 120, 151, 165, 375, 392, 405, 424] [118, 121, 152, 166, 376, 393, 406, 425] [119, 122, 153, 167, 377, 394, 407, 426] [120, 123, 154, 168, 378, 395, 408, 427] [121, 124, 155, 169, 379, 396, 409, 428] [122, 125, 156, 170, 380, 397, 410, 429] [123, 126, 157, 171, 381, 398, 411, 430] [124, 127, 158, 172, 382, 399, 412, 431] [128, 131, 162, 176, 386, 403, 416, 435] [129, 132, 163, 177, 387, 404, 417, 436] [130, 133, 164, 178, 388, 405, 418, 437] [131, 134, 165, 179, 389, 406, 419, 438] [132, 135, 166, 180, 390, 407, 420, 439] [133, 136, 167, 181, 391, 408, 421, 440] [134, 137, 168, 182, 392, 409, 422, 441] [135, 138, 169, 183, 393, 410, 423, 442] [136, 139, 170, 184, 394, 411, 424, 443] [137, 140, 171, 185, 395, 412, 425, 444] [138, 141, 172, 186, 396, 413, 426, 445] [139, 142, 173, 187, 397, 414, 427, 446] [140, 143, 174, 188, 398, 415, 428, 447] [144, 147, 178, 192, 402, 419, 432, 451] [145, 148, 179, 193, 403, 420, 433, 452] [146, 149, 180, 194, 404, 421, 434, 453] [147, 150, 181, 195, 405, 422, 435, 454] [148, 151, 182, 196, 406, 423, 436, 455] [149, 152, 183, 197, 407, 424, 437, 456] [150, 153, 184, 198, 408, 425, 438, 457] [151, 154, 185, 199, 409, 426, 439, 458] [152, 155, 186, 200, 410, 427, 440, 459] [153, 156, 187, 201, 411, 428, 441, 460] [154, 157, 188, 202, 412, 429, 442, 461] [155, 158, 189, 203, 413, 430, 443, 462] [156, 159, 190, 204, 414, 431, 444, 463] [160, 163, 194, 208, 418, 435, 448, 467] [161, 164, 195, 209, 419, 436, 449, 468] [162, 165, 196, 210, 420, 437, 450, 469] [163, 166, 197, 211, 421, 438, 451, 470] [164, 167, 198, 212, 422, 439, 452, 471] [165, 168, 199, 213, 423, 440, 453, 472] [166, 169, 200, 214, 424, 441, 454, 473] [167, 170, 201, 215, 425, 442, 455, 474] [168, 171, 202, 216, 426, 443, 456, 475] [169, 172, 203, 217, 427, 444, 457, 476] [170, 173, 204, 218, 428, 445, 458, 477] [171, 174, 205, 219, 429, 446, 459, 478] [172, 175, 206, 220, 430, 447, 460, 479] [176, 179, 210, 224, 434, 451, 464, 483] [177, 180, 211, 225, 435, 452, 465, 484] [178, 181, 212, 226, 436, 453, 466, 485] [179, 182, 213, 227, 437, 454, 467, 486] [180, 183, 214, 228, 438, 455, 468, 487] [181, 184, 215, 229, 439, 456, 469, 488] [182, 185, 216, 230, 440, 457, 470, 489] [183, 186, 217, 231, 441, 458, 471, 490] [184, 187, 218, 232, 442, 459, 472, 491] [185, 188, 219, 233, 443, 460, 473, 492] [186, 189, 220, 234, 444, 461, 474, 493] [187, 190, 221, 235, 445, 462, 475, 494] [188, 191, 222, 236, 446, 463, 476, 495] [192, 195, 226, 240, 450, 467, 480, 499] [193, 196, 227, 241, 451, 468, 481, 500] [194, 197, 228, 242, 452, 469, 482, 501] [195, 198, 229, 243, 453, 470, 483, 502] [196, 199, 230, 244, 454, 471, 484, 503] [197, 200, 231, 245, 455, 472, 485, 504] [198, 201, 232, 246, 456, 473, 486, 505] [199, 202, 233, 247, 457, 474, 487, 506] [200, 203, 234, 248, 458, 475, 488, 507] [201, 204, 235, 249, 459, 476, 489, 508] [202, 205, 236, 250, 460, 477, 490, 509] [203, 206, 237, 251, 461, 478, 491, 510] [204, 207, 238, 252, 462, 479, 492, 511] [0, 259] [1, 260] [2, 261] [3, 262] [4, 263] [5, 264] [6, 265] [7, 266] [8, 267] [9, 268] [10, 269] [11, 270] [12, 271] [2, 16, 256, 275] [3, 17, 257, 276] [4, 18, 258, 277] [5, 19, 259, 278] [6, 20, 260, 279] [7, 21, 261, 280] [8, 22, 262, 281] [9, 23, 263, 282] [10, 24, 264, 283] [11, 25, 265, 284] [12, 26, 266, 285] [13, 27, 267, 286] [14, 28, 268, 287] [3, 34, 48, 258, 259, 275, 288, 307] [4, 35, 49, 259, 260, 276, 289, 308] [5, 36, 50, 260, 261, 277, 290, 309] [6, 37, 51, 261, 262, 278, 291, 310] [7, 38, 52, 262, 263, 279, 292, 311] [8, 39, 53, 263, 264, 280, 293, 312] [9, 40, 54, 264, 265, 281, 294, 313] [10, 41, 55, 265, 266, 282, 295, 314] [11, 42, 56, 266, 267, 283, 296, 315] [12, 43, 57, 267, 268, 284, 297, 316] [13, 44, 58, 268, 269, 285, 298, 317] [14, 45, 59, 269, 270, 286, 299, 318] [15, 46, 60, 270, 271, 287, 300, 319] [18, 32, 259, 272, 291] [19, 33, 260, 273, 292] [20, 34, 261, 274, 293] [21, 35, 262, 275, 294] [22, 36, 263, 276, 295] [23, 37, 264, 277, 296] [24, 38, 265, 278, 297] [25, 39, 266, 279, 298] [26, 40, 267, 280, 299] [27, 41, 268, 281, 300] [28, 42, 269, 282, 301] [29, 43, 270, 283, 302] [30, 44, 271, 284, 303] [208, 211, 242, 466, 483, 496] [209, 212, 243, 467, 484, 497] [210, 213, 244, 468, 485, 498] [211, 214, 245, 469, 486, 499] [212, 215, 246, 470, 487, 500] [213, 216, 247, 471, 488, 501] [214, 217, 248, 472, 489, 502] [215, 218, 249, 473, 490, 503] [216, 219, 250, 474, 491, 504] [217, 220, 251, 475, 492, 505] [218, 221, 252, 476, 493, 506] [219, 222, 253, 477, 494, 507] [220, 223, 254, 478, 495, 508] [224, 227, 482, 499] [225, 228, 483, 500] [226, 229, 484, 501] [227, 230, 485, 502] [228, 231, 486, 503] [229, 232, 487, 504] [230, 233, 488, 505] [231, 234, 489, 506] [232, 235, 490, 507] [233, 236, 491, 508] [234, 237, 492, 509] [235, 238, 493, 510] [236, 239, 494, 511] [240, 243, 498] [241, 244, 499] [242, 245, 500] [243, 246, 501] [244, 247, 502] [245, 248, 503] [246, 249, 504] [247, 250, 505] [248, 251, 506] [249, 252, 507] [250, 253, 508] [251, 254, 509] [252, 255, 510]
H_Z (247 checks, sparse supports)
[0, 19, 32, 49, 259, 273, 304, 307] [1, 20, 33, 50, 260, 274, 305, 308] [2, 21, 34, 51, 261, 275, 306, 309] [3, 22, 35, 52, 262, 276, 307, 310] [4, 23, 36, 53, 263, 277, 308, 311] [5, 24, 37, 54, 264, 278, 309, 312] [6, 25, 38, 55, 265, 279, 310, 313] [7, 26, 39, 56, 266, 280, 311, 314] [8, 27, 40, 57, 267, 281, 312, 315] [9, 28, 41, 58, 268, 282, 313, 316] [10, 29, 42, 59, 269, 283, 314, 317] [11, 30, 43, 60, 270, 284, 315, 318] [12, 31, 44, 61, 271, 285, 316, 319] [16, 35, 48, 65, 275, 289, 320, 323] [17, 36, 49, 66, 276, 290, 321, 324] [18, 37, 50, 67, 277, 291, 322, 325] [19, 38, 51, 68, 278, 292, 323, 326] [20, 39, 52, 69, 279, 293, 324, 327] [21, 40, 53, 70, 280, 294, 325, 328] [22, 41, 54, 71, 281, 295, 326, 329] [23, 42, 55, 72, 282, 296, 327, 330] [24, 43, 56, 73, 283, 297, 328, 331] [25, 44, 57, 74, 284, 298, 329, 332] [26, 45, 58, 75, 285, 299, 330, 333] [27, 46, 59, 76, 286, 300, 331, 334] [28, 47, 60, 77, 287, 301, 332, 335] [32, 51, 64, 81, 291, 305, 336, 339] [33, 52, 65, 82, 292, 306, 337, 340] [34, 53, 66, 83, 293, 307, 338, 341] [35, 54, 67, 84, 294, 308, 339, 342] [36, 55, 68, 85, 295, 309, 340, 343] [37, 56, 69, 86, 296, 310, 341, 344] [38, 57, 70, 87, 297, 311, 342, 345] [39, 58, 71, 88, 298, 312, 343, 346] [40, 59, 72, 89, 299, 313, 344, 347] [41, 60, 73, 90, 300, 314, 345, 348] [42, 61, 74, 91, 301, 315, 346, 349] [43, 62, 75, 92, 302, 316, 347, 350] [44, 63, 76, 93, 303, 317, 348, 351] [48, 67, 80, 97, 307, 321, 352, 355] [49, 68, 81, 98, 308, 322, 353, 356] [50, 69, 82, 99, 309, 323, 354, 357] [51, 70, 83, 100, 310, 324, 355, 358] [52, 71, 84, 101, 311, 325, 356, 359] [53, 72, 85, 102, 312, 326, 357, 360] [54, 73, 86, 103, 313, 327, 358, 361] [55, 74, 87, 104, 314, 328, 359, 362] [56, 75, 88, 105, 315, 329, 360, 363] [57, 76, 89, 106, 316, 330, 361, 364] [58, 77, 90, 107, 317, 331, 362, 365] [59, 78, 91, 108, 318, 332, 363, 366] [60, 79, 92, 109, 319, 333, 364, 367] [64, 83, 96, 113, 323, 337, 368, 371] [65, 84, 97, 114, 324, 338, 369, 372] [66, 85, 98, 115, 325, 339, 370, 373] [67, 86, 99, 116, 326, 340, 371, 374] [68, 87, 100, 117, 327, 341, 372, 375] [69, 88, 101, 118, 328, 342, 373, 376] [70, 89, 102, 119, 329, 343, 374, 377] [71, 90, 103, 120, 330, 344, 375, 378] [72, 91, 104, 121, 331, 345, 376, 379] [73, 92, 105, 122, 332, 346, 377, 380] [74, 93, 106, 123, 333, 347, 378, 381] [75, 94, 107, 124, 334, 348, 379, 382] [76, 95, 108, 125, 335, 349, 380, 383] [80, 99, 112, 129, 339, 353, 384, 387] [81, 100, 113, 130, 340, 354, 385, 388] [82, 101, 114, 131, 341, 355, 386, 389] [83, 102, 115, 132, 342, 356, 387, 390] [84, 103, 116, 133, 343, 357, 388, 391] [85, 104, 117, 134, 344, 358, 389, 392] [86, 105, 118, 135, 345, 359, 390, 393] [87, 106, 119, 136, 346, 360, 391, 394] [88, 107, 120, 137, 347, 361, 392, 395] [89, 108, 121, 138, 348, 362, 393, 396] [90, 109, 122, 139, 349, 363, 394, 397] [91, 110, 123, 140, 350, 364, 395, 398] [92, 111, 124, 141, 351, 365, 396, 399] [96, 115, 128, 145, 355, 369, 400, 403] [97, 116, 129, 146, 356, 370, 401, 404] [98, 117, 130, 147, 357, 371, 402, 405] [99, 118, 131, 148, 358, 372, 403, 406] [100, 119, 132, 149, 359, 373, 404, 407] [101, 120, 133, 150, 360, 374, 405, 408] [102, 121, 134, 151, 361, 375, 406, 409] [103, 122, 135, 152, 362, 376, 407, 410] [104, 123, 136, 153, 363, 377, 408, 411] [105, 124, 137, 154, 364, 378, 409, 412] [106, 125, 138, 155, 365, 379, 410, 413] [107, 126, 139, 156, 366, 380, 411, 414] [108, 127, 140, 157, 367, 381, 412, 415] [112, 131, 144, 161, 371, 385, 416, 419] [113, 132, 145, 162, 372, 386, 417, 420] [114, 133, 146, 163, 373, 387, 418, 421] [115, 134, 147, 164, 374, 388, 419, 422] [116, 135, 148, 165, 375, 389, 420, 423] [117, 136, 149, 166, 376, 390, 421, 424] [118, 137, 150, 167, 377, 391, 422, 425] [119, 138, 151, 168, 378, 392, 423, 426] [120, 139, 152, 169, 379, 393, 424, 427] [121, 140, 153, 170, 380, 394, 425, 428] [122, 141, 154, 171, 381, 395, 426, 429] [123, 142, 155, 172, 382, 396, 427, 430] [124, 143, 156, 173, 383, 397, 428, 431] [128, 147, 160, 177, 387, 401, 432, 435] [129, 148, 161, 178, 388, 402, 433, 436] [130, 149, 162, 179, 389, 403, 434, 437] [131, 150, 163, 180, 390, 404, 435, 438] [132, 151, 164, 181, 391, 405, 436, 439] [133, 152, 165, 182, 392, 406, 437, 440] [134, 153, 166, 183, 393, 407, 438, 441] [135, 154, 167, 184, 394, 408, 439, 442] [136, 155, 168, 185, 395, 409, 440, 443] [137, 156, 169, 186, 396, 410, 441, 444] [138, 157, 170, 187, 397, 411, 442, 445] [139, 158, 171, 188, 398, 412, 443, 446] [140, 159, 172, 189, 399, 413, 444, 447] [144, 163, 176, 193, 403, 417, 448, 451] [145, 164, 177, 194, 404, 418, 449, 452] [146, 165, 178, 195, 405, 419, 450, 453] [147, 166, 179, 196, 406, 420, 451, 454] [148, 167, 180, 197, 407, 421, 452, 455] [149, 168, 181, 198, 408, 422, 453, 456] [150, 169, 182, 199, 409, 423, 454, 457] [151, 170, 183, 200, 410, 424, 455, 458] [152, 171, 184, 201, 411, 425, 456, 459] [153, 172, 185, 202, 412, 426, 457, 460] [154, 173, 186, 203, 413, 427, 458, 461] [155, 174, 187, 204, 414, 428, 459, 462] [156, 175, 188, 205, 415, 429, 460, 463] [160, 179, 192, 209, 419, 433, 464, 467] [161, 180, 193, 210, 420, 434, 465, 468] [162, 181, 194, 211, 421, 435, 466, 469] [163, 182, 195, 212, 422, 436, 467, 470] [164, 183, 196, 213, 423, 437, 468, 471] [165, 184, 197, 214, 424, 438, 469, 472] [166, 185, 198, 215, 425, 439, 470, 473] [167, 186, 199, 216, 426, 440, 471, 474] [168, 187, 200, 217, 427, 441, 472, 475] [169, 188, 201, 218, 428, 442, 473, 476] [170, 189, 202, 219, 429, 443, 474, 477] [171, 190, 203, 220, 430, 444, 475, 478] [172, 191, 204, 221, 431, 445, 476, 479] [176, 195, 208, 225, 435, 449, 480, 483] [177, 196, 209, 226, 436, 450, 481, 484] [178, 197, 210, 227, 437, 451, 482, 485] [179, 198, 211, 228, 438, 452, 483, 486] [180, 199, 212, 229, 439, 453, 484, 487] [181, 200, 213, 230, 440, 454, 485, 488] [182, 201, 214, 231, 441, 455, 486, 489] [183, 202, 215, 232, 442, 456, 487, 490] [184, 203, 216, 233, 443, 457, 488, 491] [185, 204, 217, 234, 444, 458, 489, 492] [186, 205, 218, 235, 445, 459, 490, 493] [187, 206, 219, 236, 446, 460, 491, 494] [188, 207, 220, 237, 447, 461, 492, 495] [192, 211, 224, 241, 451, 465, 496, 499] [193, 212, 225, 242, 452, 466, 497, 500] [194, 213, 226, 243, 453, 467, 498, 501] [195, 214, 227, 244, 454, 468, 499, 502] [196, 215, 228, 245, 455, 469, 500, 503] [197, 216, 229, 246, 456, 470, 501, 504] [198, 217, 230, 247, 457, 471, 502, 505] [199, 218, 231, 248, 458, 472, 503, 506] [200, 219, 232, 249, 459, 473, 504, 507] [201, 220, 233, 250, 460, 474, 505, 508] [202, 221, 234, 251, 461, 475, 506, 509] [203, 222, 235, 252, 462, 476, 507, 510] [204, 223, 236, 253, 463, 477, 508, 511] [16, 256, 304] [32, 272, 320] [48, 288, 336] [64, 304, 352] [80, 320, 368] [96, 336, 384] [112, 352, 400] [128, 368, 416] [144, 384, 432] [160, 400, 448] [176, 416, 464] [192, 432, 480] [208, 448, 496] [17, 257, 305] [33, 273, 321] [49, 289, 337] [65, 305, 353] [81, 321, 369] [97, 337, 385] [113, 353, 401] [129, 369, 417] [145, 385, 433] [161, 401, 449] [177, 417, 465] [193, 433, 481] [209, 449, 497] [18, 48, 258, 272, 306] [34, 64, 274, 288, 322] [50, 80, 290, 304, 338] [66, 96, 306, 320, 354] [82, 112, 322, 336, 370] [98, 128, 338, 352, 386] [114, 144, 354, 368, 402] [130, 160, 370, 384, 418] [146, 176, 386, 400, 434] [162, 192, 402, 416, 450] [178, 208, 418, 432, 466] [194, 224, 434, 448, 482] [210, 240, 450, 464, 498] [14, 46, 63, 287, 318] [30, 62, 79, 303, 334] [46, 78, 95, 319, 350] [62, 94, 111, 335, 366] [78, 110, 127, 351, 382] [94, 126, 143, 367, 398] [110, 142, 159, 383, 414] [126, 158, 175, 399, 430] [142, 174, 191, 415, 446] [158, 190, 207, 431, 462] [174, 206, 223, 447, 478] [190, 222, 239, 463, 494] [206, 238, 255, 479, 510] [13, 45, 62, 286, 317] [29, 61, 78, 302, 333] [45, 77, 94, 318, 349] [61, 93, 110, 334, 365] [77, 109, 126, 350, 381] [93, 125, 142, 366, 397] [109, 141, 158, 382, 413] [125, 157, 174, 398, 429] [141, 173, 190, 414, 445] [157, 189, 206, 430, 461] [173, 205, 222, 446, 477] [189, 221, 238, 462, 493] [205, 237, 254, 478, 509] [15, 47, 319] [31, 63, 335] [47, 79, 351] [63, 95, 367] [79, 111, 383] [95, 127, 399] [111, 143, 415] [127, 159, 431] [143, 175, 447] [159, 191, 463] [175, 207, 479] [191, 223, 495] [207, 239, 511]
Code ID 512-18-18 · download JSON · raw on GitHub