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[[882,18,29]] d ≤
n
882
k
18
d
29
kd²/n
17.163
w
8
X/Z
1.24
g
0.053
r
4.2426
layers
2
swaps
3042

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Distance

X/Z asymmetry 1.24 · d_X ≤ 36, d_Z ≤ 29 · 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 36 · witness weight 36 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified) · found at 3×108 trials · survived 3×108 trials · 2026-09-25
witness operator (support, 36 qubits)
[3, 15, 27, 33, 51, 57, 200, 222, 240, 241, 264, 281, 283, 303, 323, 347, 365, 366, 367, 384, 387, 389, 405, 409, 424, 426, 430, 558, 561, 602, 621, 643, 723, 764, 768, 806]
d_Z 29 · witness weight 29 (claimed upper_bound)
witness operator (support, 29 qubits)
[83, 143, 162, 181, 187, 200, 203, 219, 225, 241, 247, 276, 279, 282, 285, 288, 291, 295, 610, 634, 658, 672, 676, 696, 698, 718, 738, 758, 798]
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 7.04) · H_Z 3–8 (mean 7.0)
qubit degrees H_X 1–6 (mean 3.592) · H_Z 1–4 (mean 3.429)
trapping sets H_X (1,1)×60 (2,1)×148 (3,0)×54 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 60 (1,2): 118 (1,3): 66 (1,4): 531 (1,5): 92 (1,6): 15 (2,1): 148 (2,2): 183 (2,3): 485 (2,4): 884 (2,5): 681 (2,6): 6170 (2,7): 818 (2,8): 380 (2,9): 173 (2,10): 14 (3,0): 54 (3,1): 182 (3,2): 576 (3,3): 2267 (3,4): 3764 (3,5): 7755 (3,6): 17813 (3,7): 13661 (3,8): 99899 (3,9): 15317 (3,10): 17771 (3,11): 4669 (3,12): 2663 (3,13): 599 (3,14): 61
trapping sets H_Z (1,1)×63 (2,0)×18 (3,0)×18 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 63 (1,2): 126 (1,3): 63 (1,4): 630 (2,0): 18 (2,1): 137 (2,2): 269 (2,3): 445 (2,4): 898 (2,5): 702 (2,6): 7305 (3,0): 18 (3,1): 247 (3,2): 816 (3,3): 2018 (3,4): 4248 (3,5): 7951 (3,6): 19042 (3,7): 13272 (3,8): 120210 (3,9): 1155 (3,10): 13212
witness diameter X 22.8254 · Z 24.4131 (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 (441)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 3042 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 @e-eight
provenance submitted through the challenge
novelty novelty not audited
construction Open-boundary weight-8 planar bivariate-bicycle (tile) code from the half-infinite boundary engine (research/local2d/boundary_engine.py, build_planar(21,21,Sf,Sg)); Sf={(0,0),(0,3),(2,2),(3,0)}, Sg={(0,2),(1,3),(2,0),(3,3)} - the same bulk tile as codes/924-18-31.json, on a 21x21 lattice instead of 21x22. n=2*212=882, k=18, max check weight 8, interaction radius 4.2426 with layers=2. Distance is a witness-backed RIS upper bound, not exact.
model DeepSeek V4 Flash 0731 (claimed, not verified)
date 2026-09-17
notes Relation to existing entries: revision of the board's own [[882,18,30]] entry (merged PR #1149), which this entry supersedes -- same code, layout and provenance, corrected distance. A deeper fresh-seed RIS ladder turned up a weight-29 Z-logical, so the previous d <= 30 bound was inflated by one; the lightest value over all rungs is 29. It remains the small-n sibling at k = 18 of the board's [[922,18,31]] tile entry (the same bulk tile on a smaller lattice), so n and d differ and no other board entry carries this (n, k, d, w).
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

[[882,18,29]]: distance revision of the board's [[882,18,29]] entry

Revision history

The entry keeps its parameters [[882,18,29]]. The code, its checks, its layout, and its original provenance are unchanged; only the distance block is corrected. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 300,000,000 trials per side, pair depth 0, seed 4101) exhibits a weight-36 X logical, so the previous witness-backed bound was overstated on that side; the overall distance d = 29 is unchanged. Each lighter witness is carried in the entry with the budget it was found at; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

Every GPU proposal was re-validated on the CPU against the committed check matrices (in the kernel of the opposite side's checks, outside the row space of its own side) before it was recorded. The pass is the weekly fresh-seed re-measurement of the board's cell leaders (issue 2025, run of 2026-09-24); every recorded reading is the lightest CPU-verified logical at that budget.

| side | seed | claimed | GPU best weight | CPU-verified witness | trials | |---|---|---|---|---|---| | X | 4101 | 45 | 36 | 36 | 300,000,000 | | Z | 4101 | 29 | 29 | 29 | 300,000,000 | | X | 4102 | 45 | 37 | 37 | 300,000,000 | | Z | 4102 | 29 | 30 | 30 | 300,000,000 |

Original note, with the file paths updated

[[882,18,29]] — weight-8 open-boundary planar (tile) code on a 21x21 lattice

Revision history

This entry supersedes the [[882,18,30]] claim merged as PR #1149. The code, construction, layout and provenance are unchanged; only the distance claim is corrected. A deeper fresh-seed RIS ladder exhibits a lightest logical of weight 29, so the previous witness-backed bound d <= 30 was inflated by one and the honest parameter set is [[882,18,29]] (kd^2/n = 17.16). The weight-29 Z-side witness is carried in the submission; the X side records 45. Distance remains an upper bound, not an exact claim.

Direction & hypothesis

Target cell: local-2d-bilayer x weight-8, the weight-8 planar tile family whose published bar is kd^2/n ~ 12.7 (the ILP-exact [[512,18,19]], arXiv:2504.09171). The board carries the same family at larger lattices, led by [[922,18,31]] (kd^2/n = 18.761, notes/924-18-31.md) on a 21x22 lattice.

The opening this entry takes is the small-n end of that family. For this bulk tile k = 18 at every lattice size, so kd^2/n = 9 (d/L)^2: two members of the family at the same k trade n against d and can both be Pareto-non-dominated. The board had the large-n member (922 qubits, d = 31) but not a smaller-n sibling with the same tile.

What was searched

  • The B=4 tile family (research/local2d/boundary_engine.py::build_planar)

    • across L = 14..23, both square and rectangular, with the base support Sf = {(0,0),(0,3),(2,2),(3,0)}, Sg = {(0,1),(1,1),(2,0),(3,3)} — the tile of codes/578-18-20.json.

  • The two-support-swap tile of codes/924-18-31.json,

    • Sg = {(0,2),(1,3),(2,0),(3,3)}, on 21x21 (n = 882) and on 22x22, 22x20 and 20x22.

  • A 2026-09-17 follow-up sweep for a strictly better sibling: 4+4 monomial tiles

    • drawn from larger boxes (up to 5x5, i.e. up to the bilayer radius cap), an exhaustive census of the 4x4 box (all mixed-volume-18 support classes up to dihedral symmetry), and the 21x23 / 23x21 rectangles.

Evidence trail

Code: build_planar(21, 21, Sf, Sg) with the two-swap Sg; exact GF(2) rank gives n = 882, k = 18, max check weight 8, interaction radius 4.2426 at 2 layers -> local-2d-bilayer. The engine's cleanup removes no qubit.

Distance ladder (gf2_fast.distance_rand_witness, both sides searched jointly, fresh seeds; every value is an upper bound and the lightest over the ladder is the claim):

| budget | seeds | lightest found | |---|---|---| | 1M | 51, 52, 53 | 32, 32, 30 | | 3M | 54 | 30 | | 6M | 61, 62, 63 | 31, 30, 30 | | 10M | 64 | 30 | | 3M | 401, 402 | 31, 30 | | 6M | 201, 202 | 31, 31 | | 15M | 601 | 29 | | 20M | 701 | 30 |

The lightest value found over all rungs is 29 (15M, seed 601), so the claim is witness-backed upper bound d <= 29. The 1M-20M rungs are the calibration lesson of this entry: the light logical only appeared four rungs past where the original claim stopped, which is why the original d <= 30 did not hold.

The weight-29 witness was checked independently of the search backend, against the submission's own sparse checks: with H_X and H_Z rebuilt from checks, the support v satisfies H_X v = 0 (mod 2) and rank(H_Z) = 432, rank(H_Z with v appended) = 433, i.e. v is a genuine nontrivial Z-logical.

Near-misses and collapses (all rejected):

  • 22x22 (n = 968) is a screening trap. It reads 34, 33, 34 at 1M; the

    • board's own deep record for that lattice (32 at 2M, 31 at 8M and 32M in notes/924-18-31.md) makes 31 the honest value, kd^2/n = 17.87, *below* the 21x22 sibling.

  • 21x23 and 23x21 (n = 966) read 32 at 1M. A 3M follow-up ladder on 21x23 found

    • 31, so those rectangles are dominated by codes/922-18-31.json (smaller n, same k and d) and were not submitted.

  • Tiles from a 5x5 box reach k = 28..32 (mixed volume, exact GF(2) rank), but

    • they are dominated inside the n <= 1000 window: their distance slope is much shallower, so at L = 17 the best reached kd^2/n = 10.85 against 12.46 for this tile, and at the admissible maximum lattice they stay below the 21x22 point. 4x4-box tiles that beat this tile at a 20k screen (up to d <= 24 at L = 17) collapsed four units under deep RIS (33 at 300k -> 29 at 4M), another instance of the same screening inflation.

  • 21x22 with the base tile reads 27 over three seeds at 1M -> 14.88; the two-swap

    • tile is strictly better at that lattice.

Dead ends

  • Low-trial screening at n ~ 900 is inflated by 2-4, so analogue ranking at

    • 30k or 100k trials is unusable. The 22x22 row above and the 4x4-box census are the clearest cases, and are why the claim here is a deep-rung value.

  • research/local2d/transfer.py::distance_slope does not scale here. Its

    • transfer graph is exponential in the row-axis degree; a 4+4-term tile has max x-degree 3, but a min-mean cycle needs a window popcount cap above 4, at which point the state set is too large.

  • Rectangular distortion does not pay: (19,26) and (26,19) gave 24/23 at

    • 100k, and (20,22)-class rectangles were already recorded by notes/924-18-31.md as losing to the near-square ones.

  • The row-space qubit removal is not distance-preserving in general. The move

    • of notes/924-18-31.md (used for 924 -> 922) was re-tested here: on an exact time-limited MILP instance the Z-distance drops 5 -> 4 -> 3 over a chain of moves, so a greedy pass that deletes more qubits can silently lower d. It was therefore not used to chase sub-922 qubit counts.

Tools

Model DeepSeek V4 Flash 0731. numpy plus the repo's bit-packed RIS (verify/gf2_fast); construction and layout from research/local2d/boundary_engine.py and research/local2d/planar.py (grid_coordinates). Roughly 12 hours of wall clock on 16 cores.

Reproduction

Sf = [(0,0),(0,3),(2,2),(3,0)] Sg = [(0,2),(1,3),(2,0),(3,3)] HX, HZ, info = build_planar(21, 21, Sf, Sg) coords = grid_coordinates(21, 21, kept=info["kept_qubits"]) # layers = 2 # n = 882, k = 882 - rank(HX) - rank(HZ) = 18, max check weight 8

Parity checks

X-checks 450 (max weight 8) · Z-checks 432 (max weight 8)
H_X (450 checks, sparse supports)
[0, 3, 44, 63, 443, 465, 483, 507] [1, 4, 45, 64, 444, 466, 484, 508] [2, 5, 46, 65, 445, 467, 485, 509] [3, 6, 47, 66, 446, 468, 486, 510] [4, 7, 48, 67, 447, 469, 487, 511] [5, 8, 49, 68, 448, 470, 488, 512] [6, 9, 50, 69, 449, 471, 489, 513] [7, 10, 51, 70, 450, 472, 490, 514] [8, 11, 52, 71, 451, 473, 491, 515] [9, 12, 53, 72, 452, 474, 492, 516] [10, 13, 54, 73, 453, 475, 493, 517] [11, 14, 55, 74, 454, 476, 494, 518] [12, 15, 56, 75, 455, 477, 495, 519] [13, 16, 57, 76, 456, 478, 496, 520] [14, 17, 58, 77, 457, 479, 497, 521] [15, 18, 59, 78, 458, 480, 498, 522] [16, 19, 60, 79, 459, 481, 499, 523] [17, 20, 61, 80, 460, 482, 500, 524] [21, 24, 65, 84, 464, 486, 504, 528] [22, 25, 66, 85, 465, 487, 505, 529] [23, 26, 67, 86, 466, 488, 506, 530] [24, 27, 68, 87, 467, 489, 507, 531] [25, 28, 69, 88, 468, 490, 508, 532] [26, 29, 70, 89, 469, 491, 509, 533] [27, 30, 71, 90, 470, 492, 510, 534] [28, 31, 72, 91, 471, 493, 511, 535] [29, 32, 73, 92, 472, 494, 512, 536] [30, 33, 74, 93, 473, 495, 513, 537] [31, 34, 75, 94, 474, 496, 514, 538] [32, 35, 76, 95, 475, 497, 515, 539] [33, 36, 77, 96, 476, 498, 516, 540] [34, 37, 78, 97, 477, 499, 517, 541] [35, 38, 79, 98, 478, 500, 518, 542] [36, 39, 80, 99, 479, 501, 519, 543] [37, 40, 81, 100, 480, 502, 520, 544] [38, 41, 82, 101, 481, 503, 521, 545] [42, 45, 86, 105, 485, 507, 525, 549] [43, 46, 87, 106, 486, 508, 526, 550] [44, 47, 88, 107, 487, 509, 527, 551] [45, 48, 89, 108, 488, 510, 528, 552] [46, 49, 90, 109, 489, 511, 529, 553] [47, 50, 91, 110, 490, 512, 530, 554] [48, 51, 92, 111, 491, 513, 531, 555] [49, 52, 93, 112, 492, 514, 532, 556] [50, 53, 94, 113, 493, 515, 533, 557] [51, 54, 95, 114, 494, 516, 534, 558] [52, 55, 96, 115, 495, 517, 535, 559] [53, 56, 97, 116, 496, 518, 536, 560] [54, 57, 98, 117, 497, 519, 537, 561] [55, 58, 99, 118, 498, 520, 538, 562] [56, 59, 100, 119, 499, 521, 539, 563] [57, 60, 101, 120, 500, 522, 540, 564] [58, 61, 102, 121, 501, 523, 541, 565] [59, 62, 103, 122, 502, 524, 542, 566] [63, 66, 107, 126, 506, 528, 546, 570] [64, 67, 108, 127, 507, 529, 547, 571] [65, 68, 109, 128, 508, 530, 548, 572] [66, 69, 110, 129, 509, 531, 549, 573] [67, 70, 111, 130, 510, 532, 550, 574] [68, 71, 112, 131, 511, 533, 551, 575] [69, 72, 113, 132, 512, 534, 552, 576] [70, 73, 114, 133, 513, 535, 553, 577] [71, 74, 115, 134, 514, 536, 554, 578] [72, 75, 116, 135, 515, 537, 555, 579] [73, 76, 117, 136, 516, 538, 556, 580] [74, 77, 118, 137, 517, 539, 557, 581] [75, 78, 119, 138, 518, 540, 558, 582] [76, 79, 120, 139, 519, 541, 559, 583] [77, 80, 121, 140, 520, 542, 560, 584] [78, 81, 122, 141, 521, 543, 561, 585] [79, 82, 123, 142, 522, 544, 562, 586] [80, 83, 124, 143, 523, 545, 563, 587] [84, 87, 128, 147, 527, 549, 567, 591] [85, 88, 129, 148, 528, 550, 568, 592] [86, 89, 130, 149, 529, 551, 569, 593] [87, 90, 131, 150, 530, 552, 570, 594] [88, 91, 132, 151, 531, 553, 571, 595] [89, 92, 133, 152, 532, 554, 572, 596] [90, 93, 134, 153, 533, 555, 573, 597] [91, 94, 135, 154, 534, 556, 574, 598] [92, 95, 136, 155, 535, 557, 575, 599] [93, 96, 137, 156, 536, 558, 576, 600] [94, 97, 138, 157, 537, 559, 577, 601] [95, 98, 139, 158, 538, 560, 578, 602] [96, 99, 140, 159, 539, 561, 579, 603] [97, 100, 141, 160, 540, 562, 580, 604] [98, 101, 142, 161, 541, 563, 581, 605] [99, 102, 143, 162, 542, 564, 582, 606] [100, 103, 144, 163, 543, 565, 583, 607] [101, 104, 145, 164, 544, 566, 584, 608] [105, 108, 149, 168, 548, 570, 588, 612] [106, 109, 150, 169, 549, 571, 589, 613] [107, 110, 151, 170, 550, 572, 590, 614] [108, 111, 152, 171, 551, 573, 591, 615] [109, 112, 153, 172, 552, 574, 592, 616] [110, 113, 154, 173, 553, 575, 593, 617] [111, 114, 155, 174, 554, 576, 594, 618] [112, 115, 156, 175, 555, 577, 595, 619] [113, 116, 157, 176, 556, 578, 596, 620] [114, 117, 158, 177, 557, 579, 597, 621] [115, 118, 159, 178, 558, 580, 598, 622] [116, 119, 160, 179, 559, 581, 599, 623] [117, 120, 161, 180, 560, 582, 600, 624] [118, 121, 162, 181, 561, 583, 601, 625] [119, 122, 163, 182, 562, 584, 602, 626] [120, 123, 164, 183, 563, 585, 603, 627] [121, 124, 165, 184, 564, 586, 604, 628] [122, 125, 166, 185, 565, 587, 605, 629] [126, 129, 170, 189, 569, 591, 609, 633] [127, 130, 171, 190, 570, 592, 610, 634] [128, 131, 172, 191, 571, 593, 611, 635] [129, 132, 173, 192, 572, 594, 612, 636] [130, 133, 174, 193, 573, 595, 613, 637] [131, 134, 175, 194, 574, 596, 614, 638] [132, 135, 176, 195, 575, 597, 615, 639] [133, 136, 177, 196, 576, 598, 616, 640] [134, 137, 178, 197, 577, 599, 617, 641] [135, 138, 179, 198, 578, 600, 618, 642] [136, 139, 180, 199, 579, 601, 619, 643] [137, 140, 181, 200, 580, 602, 620, 644] [138, 141, 182, 201, 581, 603, 621, 645] [139, 142, 183, 202, 582, 604, 622, 646] [140, 143, 184, 203, 583, 605, 623, 647] [141, 144, 185, 204, 584, 606, 624, 648] [142, 145, 186, 205, 585, 607, 625, 649] [143, 146, 187, 206, 586, 608, 626, 650] [147, 150, 191, 210, 590, 612, 630, 654] [148, 151, 192, 211, 591, 613, 631, 655] [149, 152, 193, 212, 592, 614, 632, 656] [150, 153, 194, 213, 593, 615, 633, 657] [151, 154, 195, 214, 594, 616, 634, 658] [152, 155, 196, 215, 595, 617, 635, 659] [153, 156, 197, 216, 596, 618, 636, 660] [154, 157, 198, 217, 597, 619, 637, 661] [155, 158, 199, 218, 598, 620, 638, 662] [156, 159, 200, 219, 599, 621, 639, 663] [157, 160, 201, 220, 600, 622, 640, 664] [158, 161, 202, 221, 601, 623, 641, 665] [159, 162, 203, 222, 602, 624, 642, 666] [160, 163, 204, 223, 603, 625, 643, 667] [161, 164, 205, 224, 604, 626, 644, 668] [162, 165, 206, 225, 605, 627, 645, 669] [163, 166, 207, 226, 606, 628, 646, 670] [164, 167, 208, 227, 607, 629, 647, 671] [168, 171, 212, 231, 611, 633, 651, 675] [169, 172, 213, 232, 612, 634, 652, 676] [170, 173, 214, 233, 613, 635, 653, 677] [171, 174, 215, 234, 614, 636, 654, 678] [172, 175, 216, 235, 615, 637, 655, 679] [173, 176, 217, 236, 616, 638, 656, 680] [174, 177, 218, 237, 617, 639, 657, 681] [175, 178, 219, 238, 618, 640, 658, 682] [176, 179, 220, 239, 619, 641, 659, 683] [177, 180, 221, 240, 620, 642, 660, 684] [178, 181, 222, 241, 621, 643, 661, 685] [179, 182, 223, 242, 622, 644, 662, 686] [180, 183, 224, 243, 623, 645, 663, 687] [181, 184, 225, 244, 624, 646, 664, 688] [182, 185, 226, 245, 625, 647, 665, 689] [183, 186, 227, 246, 626, 648, 666, 690] [184, 187, 228, 247, 627, 649, 667, 691] [185, 188, 229, 248, 628, 650, 668, 692] [189, 192, 233, 252, 632, 654, 672, 696] [190, 193, 234, 253, 633, 655, 673, 697] [191, 194, 235, 254, 634, 656, 674, 698] [192, 195, 236, 255, 635, 657, 675, 699] [193, 196, 237, 256, 636, 658, 676, 700] [194, 197, 238, 257, 637, 659, 677, 701] [195, 198, 239, 258, 638, 660, 678, 702] [196, 199, 240, 259, 639, 661, 679, 703] [197, 200, 241, 260, 640, 662, 680, 704] [198, 201, 242, 261, 641, 663, 681, 705] [199, 202, 243, 262, 642, 664, 682, 706] [200, 203, 244, 263, 643, 665, 683, 707] [201, 204, 245, 264, 644, 666, 684, 708] [202, 205, 246, 265, 645, 667, 685, 709] [203, 206, 247, 266, 646, 668, 686, 710] [204, 207, 248, 267, 647, 669, 687, 711] [205, 208, 249, 268, 648, 670, 688, 712] [206, 209, 250, 269, 649, 671, 689, 713] [210, 213, 254, 273, 653, 675, 693, 717] [211, 214, 255, 274, 654, 676, 694, 718] [212, 215, 256, 275, 655, 677, 695, 719] [213, 216, 257, 276, 656, 678, 696, 720] [214, 217, 258, 277, 657, 679, 697, 721] [215, 218, 259, 278, 658, 680, 698, 722] [216, 219, 260, 279, 659, 681, 699, 723] [217, 220, 261, 280, 660, 682, 700, 724] [218, 221, 262, 281, 661, 683, 701, 725] [219, 222, 263, 282, 662, 684, 702, 726] [220, 223, 264, 283, 663, 685, 703, 727] [221, 224, 265, 284, 664, 686, 704, 728] [222, 225, 266, 285, 665, 687, 705, 729] [223, 226, 267, 286, 666, 688, 706, 730] [224, 227, 268, 287, 667, 689, 707, 731] [225, 228, 269, 288, 668, 690, 708, 732] [226, 229, 270, 289, 669, 691, 709, 733] [227, 230, 271, 290, 670, 692, 710, 734] [231, 234, 275, 294, 674, 696, 714, 738] [232, 235, 276, 295, 675, 697, 715, 739] [233, 236, 277, 296, 676, 698, 716, 740] [234, 237, 278, 297, 677, 699, 717, 741] [235, 238, 279, 298, 678, 700, 718, 742] [236, 239, 280, 299, 679, 701, 719, 743] [237, 240, 281, 300, 680, 702, 720, 744] [238, 241, 282, 301, 681, 703, 721, 745] [239, 242, 283, 302, 682, 704, 722, 746] [240, 243, 284, 303, 683, 705, 723, 747] [241, 244, 285, 304, 684, 706, 724, 748] [242, 245, 286, 305, 685, 707, 725, 749] [243, 246, 287, 306, 686, 708, 726, 750] [244, 247, 288, 307, 687, 709, 727, 751] [245, 248, 289, 308, 688, 710, 728, 752] [246, 249, 290, 309, 689, 711, 729, 753] [247, 250, 291, 310, 690, 712, 730, 754] [248, 251, 292, 311, 691, 713, 731, 755] [252, 255, 296, 315, 695, 717, 735, 759] [253, 256, 297, 316, 696, 718, 736, 760] [254, 257, 298, 317, 697, 719, 737, 761] [255, 258, 299, 318, 698, 720, 738, 762] [256, 259, 300, 319, 699, 721, 739, 763] [257, 260, 301, 320, 700, 722, 740, 764] [258, 261, 302, 321, 701, 723, 741, 765] [259, 262, 303, 322, 702, 724, 742, 766] [260, 263, 304, 323, 703, 725, 743, 767] [261, 264, 305, 324, 704, 726, 744, 768] [262, 265, 306, 325, 705, 727, 745, 769] [263, 266, 307, 326, 706, 728, 746, 770] [264, 267, 308, 327, 707, 729, 747, 771] [265, 268, 309, 328, 708, 730, 748, 772] [266, 269, 310, 329, 709, 731, 749, 773] [267, 270, 311, 330, 710, 732, 750, 774] [268, 271, 312, 331, 711, 733, 751, 775] [269, 272, 313, 332, 712, 734, 752, 776] [273, 276, 317, 336, 716, 738, 756, 780] [274, 277, 318, 337, 717, 739, 757, 781] [275, 278, 319, 338, 718, 740, 758, 782] [276, 279, 320, 339, 719, 741, 759, 783] [277, 280, 321, 340, 720, 742, 760, 784] [278, 281, 322, 341, 721, 743, 761, 785] [279, 282, 323, 342, 722, 744, 762, 786] [280, 283, 324, 343, 723, 745, 763, 787] [281, 284, 325, 344, 724, 746, 764, 788] [282, 285, 326, 345, 725, 747, 765, 789] [283, 286, 327, 346, 726, 748, 766, 790] [284, 287, 328, 347, 727, 749, 767, 791] [285, 288, 329, 348, 728, 750, 768, 792] [286, 289, 330, 349, 729, 751, 769, 793] [287, 290, 331, 350, 730, 752, 770, 794] [288, 291, 332, 351, 731, 753, 771, 795] [289, 292, 333, 352, 732, 754, 772, 796] [290, 293, 334, 353, 733, 755, 773, 797] [294, 297, 338, 357, 737, 759, 777, 801] [295, 298, 339, 358, 738, 760, 778, 802] [296, 299, 340, 359, 739, 761, 779, 803] [297, 300, 341, 360, 740, 762, 780, 804] [298, 301, 342, 361, 741, 763, 781, 805] [299, 302, 343, 362, 742, 764, 782, 806] [300, 303, 344, 363, 743, 765, 783, 807] [301, 304, 345, 364, 744, 766, 784, 808] [302, 305, 346, 365, 745, 767, 785, 809] [303, 306, 347, 366, 746, 768, 786, 810] [304, 307, 348, 367, 747, 769, 787, 811] [305, 308, 349, 368, 748, 770, 788, 812] [306, 309, 350, 369, 749, 771, 789, 813] [307, 310, 351, 370, 750, 772, 790, 814] [308, 311, 352, 371, 751, 773, 791, 815] [309, 312, 353, 372, 752, 774, 792, 816] [310, 313, 354, 373, 753, 775, 793, 817] [311, 314, 355, 374, 754, 776, 794, 818] [315, 318, 359, 378, 758, 780, 798, 822] [316, 319, 360, 379, 759, 781, 799, 823] [317, 320, 361, 380, 760, 782, 800, 824] [318, 321, 362, 381, 761, 783, 801, 825] [319, 322, 363, 382, 762, 784, 802, 826] [320, 323, 364, 383, 763, 785, 803, 827] [321, 324, 365, 384, 764, 786, 804, 828] [322, 325, 366, 385, 765, 787, 805, 829] [323, 326, 367, 386, 766, 788, 806, 830] [324, 327, 368, 387, 767, 789, 807, 831] [325, 328, 369, 388, 768, 790, 808, 832] [326, 329, 370, 389, 769, 791, 809, 833] [327, 330, 371, 390, 770, 792, 810, 834] [328, 331, 372, 391, 771, 793, 811, 835] [329, 332, 373, 392, 772, 794, 812, 836] [330, 333, 374, 393, 773, 795, 813, 837] [331, 334, 375, 394, 774, 796, 814, 838] [332, 335, 376, 395, 775, 797, 815, 839] [336, 339, 380, 399, 779, 801, 819, 843] [337, 340, 381, 400, 780, 802, 820, 844] [338, 341, 382, 401, 781, 803, 821, 845] [339, 342, 383, 402, 782, 804, 822, 846] [340, 343, 384, 403, 783, 805, 823, 847] [341, 344, 385, 404, 784, 806, 824, 848] [342, 345, 386, 405, 785, 807, 825, 849] [343, 346, 387, 406, 786, 808, 826, 850] [344, 347, 388, 407, 787, 809, 827, 851] [345, 348, 389, 408, 788, 810, 828, 852] [346, 349, 390, 409, 789, 811, 829, 853] [347, 350, 391, 410, 790, 812, 830, 854] [348, 351, 392, 411, 791, 813, 831, 855] [349, 352, 393, 412, 792, 814, 832, 856] [350, 353, 394, 413, 793, 815, 833, 857] [351, 354, 395, 414, 794, 816, 834, 858] [352, 355, 396, 415, 795, 817, 835, 859] [353, 356, 397, 416, 796, 818, 836, 860] [357, 360, 401, 420, 800, 822, 840, 864] [358, 361, 402, 421, 801, 823, 841, 865] [359, 362, 403, 422, 802, 824, 842, 866] [360, 363, 404, 423, 803, 825, 843, 867] [361, 364, 405, 424, 804, 826, 844, 868] [362, 365, 406, 425, 805, 827, 845, 869] [363, 366, 407, 426, 806, 828, 846, 870] [364, 367, 408, 427, 807, 829, 847, 871] [365, 368, 409, 428, 808, 830, 848, 872] [366, 369, 410, 429, 809, 831, 849, 873] [367, 370, 411, 430, 810, 832, 850, 874] [368, 371, 412, 431, 811, 833, 851, 875] [369, 372, 413, 432, 812, 834, 852, 876] [370, 373, 414, 433, 813, 835, 853, 877] [371, 374, 415, 434, 814, 836, 854, 878] [372, 375, 416, 435, 815, 837, 855, 879] [373, 376, 417, 436, 816, 838, 856, 880] [374, 377, 418, 437, 817, 839, 857, 881] [0, 444] [1, 445] [2, 446] [3, 447] [4, 448] [5, 449] [6, 450] [7, 451] [8, 452] [9, 453] [10, 454] [11, 455] [12, 456] [13, 457] [14, 458] [15, 459] [16, 460] [17, 461] [2, 21, 441, 465] [3, 22, 442, 466] [4, 23, 443, 467] [5, 24, 444, 468] [6, 25, 445, 469] [7, 26, 446, 470] [8, 27, 447, 471] [9, 28, 448, 472] [10, 29, 449, 473] [11, 30, 450, 474] [12, 31, 451, 475] [13, 32, 452, 476] [14, 33, 453, 477] [15, 34, 454, 478] [16, 35, 455, 479] [17, 36, 456, 480] [18, 37, 457, 481] [19, 38, 458, 482] [3, 44, 63, 443, 444, 465, 483, 507] [4, 45, 64, 444, 445, 466, 484, 508] [5, 46, 65, 445, 446, 467, 485, 509] [6, 47, 66, 446, 447, 468, 486, 510] [7, 48, 67, 447, 448, 469, 487, 511] [8, 49, 68, 448, 449, 470, 488, 512] [9, 50, 69, 449, 450, 471, 489, 513] [10, 51, 70, 450, 451, 472, 490, 514] [11, 52, 71, 451, 452, 473, 491, 515] [12, 53, 72, 452, 453, 474, 492, 516] [13, 54, 73, 453, 454, 475, 493, 517] [14, 55, 74, 454, 455, 476, 494, 518] [15, 56, 75, 455, 456, 477, 495, 519] [16, 57, 76, 456, 457, 478, 496, 520] [17, 58, 77, 457, 458, 479, 497, 521] [18, 59, 78, 458, 459, 480, 498, 522] [19, 60, 79, 459, 460, 481, 499, 523] [20, 61, 80, 460, 461, 482, 500, 524] [23, 42, 444, 462, 486] [24, 43, 445, 463, 487] [25, 44, 446, 464, 488] [26, 45, 447, 465, 489] [27, 46, 448, 466, 490] [28, 47, 449, 467, 491] [29, 48, 450, 468, 492] [30, 49, 451, 469, 493] [31, 50, 452, 470, 494] [32, 51, 453, 471, 495] [33, 52, 454, 472, 496] [34, 53, 455, 473, 497] [35, 54, 456, 474, 498] [36, 55, 457, 475, 499] [37, 56, 458, 476, 500] [38, 57, 459, 477, 501] [39, 58, 460, 478, 502] [40, 59, 461, 479, 503] [378, 381, 422, 821, 843, 861] [379, 382, 423, 822, 844, 862] [380, 383, 424, 823, 845, 863] [381, 384, 425, 824, 846, 864] [382, 385, 426, 825, 847, 865] [383, 386, 427, 826, 848, 866] [384, 387, 428, 827, 849, 867] [385, 388, 429, 828, 850, 868] [386, 389, 430, 829, 851, 869] [387, 390, 431, 830, 852, 870] [388, 391, 432, 831, 853, 871] [389, 392, 433, 832, 854, 872] [390, 393, 434, 833, 855, 873] [391, 394, 435, 834, 856, 874] [392, 395, 436, 835, 857, 875] [393, 396, 437, 836, 858, 876] [394, 397, 438, 837, 859, 877] [395, 398, 439, 838, 860, 878] [399, 402, 842, 864] [400, 403, 843, 865] [401, 404, 844, 866] [402, 405, 845, 867] [403, 406, 846, 868] [404, 407, 847, 869] [405, 408, 848, 870] [406, 409, 849, 871] [407, 410, 850, 872] [408, 411, 851, 873] [409, 412, 852, 874] [410, 413, 853, 875] [411, 414, 854, 876] [412, 415, 855, 877] [413, 416, 856, 878] [414, 417, 857, 879] [415, 418, 858, 880] [416, 419, 859, 881] [420, 423, 863] [421, 424, 864] [422, 425, 865] [423, 426, 866] [424, 427, 867] [425, 428, 868] [426, 429, 869] [427, 430, 870] [428, 431, 871] [429, 432, 872] [430, 433, 873] [431, 434, 874] [432, 435, 875] [433, 436, 876] [434, 437, 877] [435, 438, 878] [436, 439, 879] [437, 440, 880]
H_Z (432 checks, sparse supports)
[0, 24, 42, 64, 444, 463, 504, 507] [1, 25, 43, 65, 445, 464, 505, 508] [2, 26, 44, 66, 446, 465, 506, 509] [3, 27, 45, 67, 447, 466, 507, 510] [4, 28, 46, 68, 448, 467, 508, 511] [5, 29, 47, 69, 449, 468, 509, 512] [6, 30, 48, 70, 450, 469, 510, 513] [7, 31, 49, 71, 451, 470, 511, 514] [8, 32, 50, 72, 452, 471, 512, 515] [9, 33, 51, 73, 453, 472, 513, 516] [10, 34, 52, 74, 454, 473, 514, 517] [11, 35, 53, 75, 455, 474, 515, 518] [12, 36, 54, 76, 456, 475, 516, 519] [13, 37, 55, 77, 457, 476, 517, 520] [14, 38, 56, 78, 458, 477, 518, 521] [15, 39, 57, 79, 459, 478, 519, 522] [16, 40, 58, 80, 460, 479, 520, 523] [17, 41, 59, 81, 461, 480, 521, 524] [21, 45, 63, 85, 465, 484, 525, 528] [22, 46, 64, 86, 466, 485, 526, 529] [23, 47, 65, 87, 467, 486, 527, 530] [24, 48, 66, 88, 468, 487, 528, 531] [25, 49, 67, 89, 469, 488, 529, 532] [26, 50, 68, 90, 470, 489, 530, 533] [27, 51, 69, 91, 471, 490, 531, 534] [28, 52, 70, 92, 472, 491, 532, 535] [29, 53, 71, 93, 473, 492, 533, 536] [30, 54, 72, 94, 474, 493, 534, 537] [31, 55, 73, 95, 475, 494, 535, 538] [32, 56, 74, 96, 476, 495, 536, 539] [33, 57, 75, 97, 477, 496, 537, 540] [34, 58, 76, 98, 478, 497, 538, 541] [35, 59, 77, 99, 479, 498, 539, 542] [36, 60, 78, 100, 480, 499, 540, 543] [37, 61, 79, 101, 481, 500, 541, 544] [38, 62, 80, 102, 482, 501, 542, 545] [42, 66, 84, 106, 486, 505, 546, 549] [43, 67, 85, 107, 487, 506, 547, 550] [44, 68, 86, 108, 488, 507, 548, 551] [45, 69, 87, 109, 489, 508, 549, 552] [46, 70, 88, 110, 490, 509, 550, 553] [47, 71, 89, 111, 491, 510, 551, 554] [48, 72, 90, 112, 492, 511, 552, 555] [49, 73, 91, 113, 493, 512, 553, 556] [50, 74, 92, 114, 494, 513, 554, 557] [51, 75, 93, 115, 495, 514, 555, 558] [52, 76, 94, 116, 496, 515, 556, 559] [53, 77, 95, 117, 497, 516, 557, 560] [54, 78, 96, 118, 498, 517, 558, 561] [55, 79, 97, 119, 499, 518, 559, 562] [56, 80, 98, 120, 500, 519, 560, 563] [57, 81, 99, 121, 501, 520, 561, 564] [58, 82, 100, 122, 502, 521, 562, 565] [59, 83, 101, 123, 503, 522, 563, 566] [63, 87, 105, 127, 507, 526, 567, 570] [64, 88, 106, 128, 508, 527, 568, 571] [65, 89, 107, 129, 509, 528, 569, 572] [66, 90, 108, 130, 510, 529, 570, 573] [67, 91, 109, 131, 511, 530, 571, 574] [68, 92, 110, 132, 512, 531, 572, 575] [69, 93, 111, 133, 513, 532, 573, 576] [70, 94, 112, 134, 514, 533, 574, 577] [71, 95, 113, 135, 515, 534, 575, 578] [72, 96, 114, 136, 516, 535, 576, 579] [73, 97, 115, 137, 517, 536, 577, 580] [74, 98, 116, 138, 518, 537, 578, 581] [75, 99, 117, 139, 519, 538, 579, 582] [76, 100, 118, 140, 520, 539, 580, 583] [77, 101, 119, 141, 521, 540, 581, 584] [78, 102, 120, 142, 522, 541, 582, 585] [79, 103, 121, 143, 523, 542, 583, 586] [80, 104, 122, 144, 524, 543, 584, 587] [84, 108, 126, 148, 528, 547, 588, 591] [85, 109, 127, 149, 529, 548, 589, 592] [86, 110, 128, 150, 530, 549, 590, 593] [87, 111, 129, 151, 531, 550, 591, 594] [88, 112, 130, 152, 532, 551, 592, 595] [89, 113, 131, 153, 533, 552, 593, 596] [90, 114, 132, 154, 534, 553, 594, 597] [91, 115, 133, 155, 535, 554, 595, 598] [92, 116, 134, 156, 536, 555, 596, 599] [93, 117, 135, 157, 537, 556, 597, 600] [94, 118, 136, 158, 538, 557, 598, 601] [95, 119, 137, 159, 539, 558, 599, 602] [96, 120, 138, 160, 540, 559, 600, 603] [97, 121, 139, 161, 541, 560, 601, 604] [98, 122, 140, 162, 542, 561, 602, 605] [99, 123, 141, 163, 543, 562, 603, 606] [100, 124, 142, 164, 544, 563, 604, 607] [101, 125, 143, 165, 545, 564, 605, 608] [105, 129, 147, 169, 549, 568, 609, 612] [106, 130, 148, 170, 550, 569, 610, 613] [107, 131, 149, 171, 551, 570, 611, 614] [108, 132, 150, 172, 552, 571, 612, 615] [109, 133, 151, 173, 553, 572, 613, 616] [110, 134, 152, 174, 554, 573, 614, 617] [111, 135, 153, 175, 555, 574, 615, 618] [112, 136, 154, 176, 556, 575, 616, 619] [113, 137, 155, 177, 557, 576, 617, 620] [114, 138, 156, 178, 558, 577, 618, 621] [115, 139, 157, 179, 559, 578, 619, 622] [116, 140, 158, 180, 560, 579, 620, 623] [117, 141, 159, 181, 561, 580, 621, 624] [118, 142, 160, 182, 562, 581, 622, 625] [119, 143, 161, 183, 563, 582, 623, 626] [120, 144, 162, 184, 564, 583, 624, 627] [121, 145, 163, 185, 565, 584, 625, 628] [122, 146, 164, 186, 566, 585, 626, 629] [126, 150, 168, 190, 570, 589, 630, 633] [127, 151, 169, 191, 571, 590, 631, 634] [128, 152, 170, 192, 572, 591, 632, 635] [129, 153, 171, 193, 573, 592, 633, 636] [130, 154, 172, 194, 574, 593, 634, 637] [131, 155, 173, 195, 575, 594, 635, 638] [132, 156, 174, 196, 576, 595, 636, 639] [133, 157, 175, 197, 577, 596, 637, 640] [134, 158, 176, 198, 578, 597, 638, 641] [135, 159, 177, 199, 579, 598, 639, 642] [136, 160, 178, 200, 580, 599, 640, 643] [137, 161, 179, 201, 581, 600, 641, 644] [138, 162, 180, 202, 582, 601, 642, 645] [139, 163, 181, 203, 583, 602, 643, 646] [140, 164, 182, 204, 584, 603, 644, 647] [141, 165, 183, 205, 585, 604, 645, 648] [142, 166, 184, 206, 586, 605, 646, 649] [143, 167, 185, 207, 587, 606, 647, 650] [147, 171, 189, 211, 591, 610, 651, 654] [148, 172, 190, 212, 592, 611, 652, 655] [149, 173, 191, 213, 593, 612, 653, 656] [150, 174, 192, 214, 594, 613, 654, 657] [151, 175, 193, 215, 595, 614, 655, 658] [152, 176, 194, 216, 596, 615, 656, 659] [153, 177, 195, 217, 597, 616, 657, 660] [154, 178, 196, 218, 598, 617, 658, 661] [155, 179, 197, 219, 599, 618, 659, 662] [156, 180, 198, 220, 600, 619, 660, 663] [157, 181, 199, 221, 601, 620, 661, 664] [158, 182, 200, 222, 602, 621, 662, 665] [159, 183, 201, 223, 603, 622, 663, 666] [160, 184, 202, 224, 604, 623, 664, 667] [161, 185, 203, 225, 605, 624, 665, 668] [162, 186, 204, 226, 606, 625, 666, 669] [163, 187, 205, 227, 607, 626, 667, 670] [164, 188, 206, 228, 608, 627, 668, 671] [168, 192, 210, 232, 612, 631, 672, 675] [169, 193, 211, 233, 613, 632, 673, 676] [170, 194, 212, 234, 614, 633, 674, 677] [171, 195, 213, 235, 615, 634, 675, 678] [172, 196, 214, 236, 616, 635, 676, 679] [173, 197, 215, 237, 617, 636, 677, 680] [174, 198, 216, 238, 618, 637, 678, 681] [175, 199, 217, 239, 619, 638, 679, 682] [176, 200, 218, 240, 620, 639, 680, 683] [177, 201, 219, 241, 621, 640, 681, 684] [178, 202, 220, 242, 622, 641, 682, 685] [179, 203, 221, 243, 623, 642, 683, 686] [180, 204, 222, 244, 624, 643, 684, 687] [181, 205, 223, 245, 625, 644, 685, 688] [182, 206, 224, 246, 626, 645, 686, 689] [183, 207, 225, 247, 627, 646, 687, 690] [184, 208, 226, 248, 628, 647, 688, 691] [185, 209, 227, 249, 629, 648, 689, 692] [189, 213, 231, 253, 633, 652, 693, 696] [190, 214, 232, 254, 634, 653, 694, 697] [191, 215, 233, 255, 635, 654, 695, 698] [192, 216, 234, 256, 636, 655, 696, 699] [193, 217, 235, 257, 637, 656, 697, 700] [194, 218, 236, 258, 638, 657, 698, 701] [195, 219, 237, 259, 639, 658, 699, 702] [196, 220, 238, 260, 640, 659, 700, 703] [197, 221, 239, 261, 641, 660, 701, 704] [198, 222, 240, 262, 642, 661, 702, 705] [199, 223, 241, 263, 643, 662, 703, 706] [200, 224, 242, 264, 644, 663, 704, 707] [201, 225, 243, 265, 645, 664, 705, 708] [202, 226, 244, 266, 646, 665, 706, 709] [203, 227, 245, 267, 647, 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Code ID 882-18-29 · download JSON · raw on GitHub