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[[512,18,19]] d ≤
n
512
k
18
d
19
kd²/n
12.691
w
8
X/Z
1.05
g
0.011
r
5.831
layers
2
swaps
1793

Share this result

Distance

X/Z asymmetry 1.05 · d_X ≤ 19, d_Z ≤ 20 · 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 19 · witness weight 19 (claimed upper_bound)
witness found by @MathysRennela · research/kit/surrogate.distance_rand_witness (gf2_fast backend) · found at 1.2×106 trials · survived 1.2×106 trials · 2026-10-10
witness operator (support, 19 qubits)
[20, 46, 251, 270, 282, 316, 327, 350, 361, 375, 378, 381, 395, 412, 423, 443, 457, 471, 474]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness found by @MathysRennela · research/kit/surrogate._search_lightest (numpy, pair_depth 24) · found at 6000 trials · survived 6000 trials · 2026-10-10
witness operator (support, 20 qubits)
[127, 155, 169, 172, 178, 181, 183, 186, 189, 370, 386, 400, 401, 404, 405, 414, 421, 437, 438, 479]
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 4 (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 2–8 (mean 6.748)
qubit degrees H_X 1–6 (mean 3.453) · H_Z 1–6 (mean 3.4)
trapping sets H_X (1,1)×58 (2,0)×13 (3,0)×37 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 58 (1,2): 64 (1,3): 61 (1,4): 266 (1,5): 43 (1,6): 20 (2,0): 13 (2,1): 81 (2,2): 134 (2,3): 388 (2,4): 642 (2,5): 542 (2,6): 2588 (2,7): 468 (2,8): 225 (2,9): 80 (2,10): 32 (3,0): 37 (3,1): 109 (3,2): 510 (3,3): 1435 (3,4): 2872 (3,5): 5846 (3,6): 11705 (3,7): 9637 (3,8): 36614 (3,9): 8157 (3,10): 7227 (3,11): 2246 (3,12): 1253 (3,13): 431 (3,14): 83
trapping sets H_Z (1,1)×61 (2,0)×13 (3,0)×37 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 61 (1,2): 59 (1,3): 67 (1,4): 270 (1,5): 49 (1,6): 6 (2,0): 13 (2,1): 81 (2,2): 134 (2,3): 397 (2,4): 643 (2,5): 556 (2,6): 2608 (2,7): 512 (2,8): 204 (2,9): 71 (2,10): 4 (3,0): 37 (3,1): 106 (3,2): 513 (3,3): 1460 (3,4): 2909 (3,5): 5941 (3,6): 11834 (3,7): 9832 (3,8): 36874 (3,9): 8565 (3,10): 7557 (3,11): 2443 (3,12): 1160 (3,13): 179 (3,14): 22 (3,15): 1
witness diameter X 15.6525 · Z 15.5242 (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 = 5.831
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 1793 nearest-neighbor SWAPs per round in total, at most 7 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 Steffan, Vincent and Choe, Shin Ho and Breuckmann, Nikolas P. and Pereira, Francisco Revson Fernandes and Eberhardt, Jens Niklas
provenance literature baseline
construction Published tile code of arXiv:2504.09171 (Table 1, [[512,18,19]]), rebuilt from the paper's own specification. Open boundary, B=4 boxes, weight-8 tiles, unrotated square layout of 13x13 bulk tiles -> a 16x16 qubit lattice, 2 qubits per site, n=512, k=18. Tile supports taken verbatim from the arXiv LaTeX source (main.tex lines 690-691, repeated at 763-764), which carries them as literal \def macros rather than 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)}, with the Z-tile the (B-1-x, B-1-y) reflection of the X-tile with the edge orientation swapped (the paper's condition T2). Built with this repo's research/local2d/boundary_engine.build_planar(16,16,S_F_TILE4,((0,1),(1,0),(1,1),(3,3))). That call additionally 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 the rows of weight > 8 are dropped to recover the paper's weight-8 stabilizer set. Layout is research/local2d/planar.grid_coordinates(16,16,kept=info['kept_qubits']) with layers=2. Calibration: the same tile at 9x9 bulk (a 12x12 qubit lattice) reproduces the paper's other B=4 weight-8 entry, [[288,18,13]], at a witnessed d <= 13.
model Space Bunny Alpha 1.0 (claimed, not verified)
reference arXiv:2504.09171
date 2026-10-10
notes Literature baseline, seeded 2026-10-10. arXiv:2504.09171 states d=19 exactly (ILP); recorded here as a witness-backed upper bound (d<=19) pending this repo's own server certification. The bound rests on the X side: a weight-19 logical at 1,200,000 accelerator trials, and nothing lighter was found there or on the Z side. The Z-side witness was screened more shallowly (6,000 NumPy trials) because the accelerator reports only the lighter of the two sides and the X side is the one that bounds the claim; the Z weight only has to be at least the X weight for min(d_X,d_Z) to stay at 19. Calibration is by the paper's SECOND published B=4 weight-8 code, [[288,18,13]] at 9x9 bulk, where the identical tile reproduces d<=13: the generator matches the paper at two independent published exact distances, not one. This is NOT the code behind the board's S_G_TILE4_MAIN entries (codes/800-18-27.json, codes/882-18-29.json, codes/924-18-31.json, codes/968-18-31.json), which carry arXiv:2504.09171 in their provenance. That B-support differs from the published tile in three of four monomials and reproduces d<=18 here, one below the paper. Nor is it the sibling support those entries record, ((0,1),(1,1),(2,0),(3,3)), which differs from the published tile in one monomial and gives d<=11 at 12x12.
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

[[512,18,19]] — literature baseline: the tile code of arXiv:2504.09171, rebuilt from the paper's own source

A literature baseline, so this note documents the reproduction rather than a search (see CONTRIBUTING.md). There was no search here: the code is published, the question was only whether it could be rebuilt from what the paper actually ships.

What is being seeded

arXiv:2504.09171 (Steffan, Choe, Breuckmann, Pereira, Eberhardt), Table 1, reports [[512,18,19]] with d=19 stated exact from an integer linear program. The entry here reproduces it as a witness-backed upper bound, d <= 19. It is not a new code and claims no novelty; it exists so the board stops citing a bar it has never measured.

Where the specification lives

The paper's tiles appear in its LaTeX source as literal \def macros, not only in a figure — main.tex lines 690-691, repeated verbatim at 763-764 for the second code in the same row of Table 1:

\def\horizontalqubits{(0, 0), (0, 3), (2, 2), (3, 0)}
\def\verticalqubits{(0, 1), (1, 0), (1, 1), (3, 3)}
\def\boxsize{4}

The Z-tile is not a free choice: it is the (B-1-x, B-1-y) reflection of the X-tile with the edge orientation swapped, which is the paper's condition (T2) and the reason the bulk terms commute. Geometry is in the text — 13x13 bulk tiles, and with B=4 a 16x16 qubit lattice at 2 qubits per site, so n = 2*L*L = 512.

Reproduction

research/local2d/boundary_engine.build_planar(
    16, 16, S_F_TILE4, ((0, 1), (1, 0), (1, 1), (3, 3)))

with S_F_TILE4 = ((0,0),(0,3),(2,2),(3,0)), a module constant. Layout is research/local2d/planar.grid_coordinates(16, 16, kept=info['kept_qubits']) with layers=2: 512 coordinates over 256 sites, interaction radius 4.2426 = 3*sqrt(2), which clears the 4.0 single-layer cap and sits inside the 7.0 bilayer cap.

One wrinkle is worth writing down, because it is not obvious from the call. That build emits 48 Z-boundary stabilizers of weight 12-18 on top of the weight-8 ones. All of them lie in the row space of the weight-8 rows — rank 247 either way — so they are redundant rather than additional. Dropping every row of weight > 8 recovers the paper's weight-8 stabilizer set and leaves the code space unchanged. A naive max-check-weight read on the untrimmed build says 18, and would file the entry in the wrong weight class.

Why this is not the code already on the board

Four entries carry this paper in their provenance: codes/800-18-27.json, codes/882-18-29.json, codes/924-18-31.json, codes/968-18-31.json. They use B-support ((0,2),(1,3),(2,0),(3,3)), which differs from the published vertical set in three of four monomials. The sibling support recorded by codes/566-18-20.json, ((0,1),(1,1),(2,0),(3,3)), differs from the published one in a single monomial — that is the "one support swap" codes/578-18-20.json describes. All three are different codes from the published tile.

Measured, each side witness-validated with verify/qldpc_verify.py's own gf2.commutes / gf2.in_rowspace:

| B-support | 12x12 — paper [[288,18,13]], d=13 | 16x16 — paper [[512,18,19]], d=19 | | --- | --- | --- | | published tile (this entry) | d <= 13 | d <= 19 | | ((0,2),(1,3),(2,0),(3,3)) | d <= 11 | d <= 18 | | ((0,1),(1,1),(2,0),(3,3)) | d <= 11 | d <= 18 |

The published tile landing on both of the paper's exact distances, at two independent sizes, is what identifies it. The other two landing one to two below at both sizes is the signature of a different code rather than of a mis-measurement.

The transferable lesson from this is worth stating here, since it is the reason the mis-identification survived for so long. Check-matrix calibration cannot catch it: the four board entries reproduce their generator row for row and are still not the published code, so the only thing that separated the two was a distance the literature had published and the board had not. Calibrate against a number the *literature* published, and at a second size if the paper gives one. A generator that lands on two independent exact values has been checked against something external; a generator that reproduces its own entries has only been checked against itself.

Distance claim and its budget

d <= 19, upper_bound, not certified exact. The paper's exactness rests on its own ILP; certifying here is the maintainer-side verify/certify.py tier and is not asserted. Nothing in this entry claims a logical lighter than 19 exists.

  • X side — weight-19 witness from research/kit/surrogate.distance_rand_witness

    • on the gf2_fast accelerator, 1,200,000 trials across two seeds. This is the witness the bound rests on.

  • Z side — weight-20 witness from the NumPy per-side path at 6,000 trials,

    • pair_depth 24. Deliberately shallower: the accelerator reports only the lighter of the two sides, and since the X side is the lighter, it never surfaces a Z witness on its own. The Z weight only has to be at least the X weight for min(d_X, d_Z) to stay at 19, and the X witness alone proves d <= 19 whatever the Z side turns out to be. The asymmetry is recorded in each side's witness_provenance rather than smoothed over.

Both witnesses were re-checked against the verifier's criteria before packaging, not taken on the surrogate's word.

Tools

Model: Space Bunny Alpha 1.0 (opencode). research/local2d/boundary_engine.py, research/local2d/planar.py, research/kit/surrogate.py, research/kit/submit.py, research/kit/coordination.py, verify/gf2_fast. Verdict from verify/validate_candidate.py via coordination.py gate: passed: true, board_advancing: true, advances_by: ["n"], no duplicate by fingerprint or Weisfeiler-Leman signature. Compute: CPU only.

Parity checks

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