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[[796,8,27]] d ≤
n
796
k
8
d
27
kd²/n
7.327
w
8
X/Z
1
g
0.115
r
4.0
layers
1
swaps
1518

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Distance

X/Z asymmetry 1 · d_X ≤ 27, d_Z ≤ 27 · 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 27 · witness weight 27 (claimed upper_bound)
witness found by @dorakingx and @vprusso · Clifford image of codes/798-8-27.json logical · found at 2×105 trials · 2026-10-13
witness operator (support, 27 qubits)
[83, 246, 267, 308, 328, 347, 367, 397, 416, 437, 479, 480, 481, 501, 520, 521, 522, 541, 563, 583, 604, 664, 665, 666, 684, 686, 765]
d_Z 27 · witness weight 27 (claimed upper_bound)
witness found by @vprusso · Clifford image of PR #3385 Z logical · found at 1 trials · 2026-10-13
witness operator (support, 27 qubits)
[140, 161, 162, 181, 185, 205, 206, 207, 208, 214, 216, 229, 231, 235, 236, 556, 558, 580, 581, 604, 611, 612, 628, 629, 630, 631, 634]
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 3–8 (mean 7.301) · H_Z 2–8 (mean 7.25)
qubit degrees H_X 1–6 (mean 3.595) · H_Z 1–4 (mean 3.607)
trapping sets H_X (1,1)×62 (2,0)×22 (3,0)×17 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 62 (1,2): 41 (1,3): 57 (1,4): 634 (1,5): 1 (1,6): 1 (2,0): 22 (2,1): 97 (2,2): 183 (2,3): 398 (2,4): 1768 (2,5): 385 (2,6): 4993 (2,7): 7 (2,8): 9 (3,0): 17 (3,1): 187 (3,2): 761 (3,3): 1807 (3,4): 4704 (3,5): 5708 (3,6): 33465 (3,7): 4682 (3,8): 57720 (3,9): 318 (3,10): 3953 (3,11): 2 (3,12): 4
trapping sets H_Z (1,1)×38 (2,1)×124 (3,0)×33 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 38 (1,2): 80 (1,3): 39 (1,4): 639 (2,1): 124 (2,2): 210 (2,3): 394 (2,4): 1904 (2,5): 224 (2,6): 5034 (3,0): 33 (3,1): 191 (3,2): 657 (3,3): 2021 (3,4): 5366 (3,5): 5190 (3,6): 34881 (3,7): 3150 (3,8): 58211 (3,9): 90 (3,10): 3902
witness diameter X 28.7924 · Z 25.807 (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
X checkZ checkqubit site (796)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 1518 nearest-neighbor SWAPs per round in total, at most 3 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 @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Two disjoint X-side four-check row-space grafts of codes/798-8-27.json by @dorakingx. First XOR source rows [360,376,377,378] to form S1=[360,361,378,762,781,782], pivot row 376, remove qubit 378. Then XOR source rows [0,1,18,19] to form S2=[1,3,21,22,399,400,418,420], pivot row 0, remove source qubit 399 (index 398 after the first reduction). For each graft replace the pivot by S, clear its target qubit from other X rows using S, apply CNOT fanout from the target to S\{target}, and delete the disentangled qubit. Retain source coordinates of surviving qubits.
model GPT-6 (Codex) (claimed, not verified)
builds on arXiv:2504.08887
date 2026-10-13
notes Two independent local row-space grafts lower n from 798 to 796 while preserving k=8, check weight 8, radius 4, and witnessed X-27 and Z-27 logicals. Distance is a witnessed upper bound, not an exact claim.
family tile (a tag, not a ranking)
locality 2D-local single (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

[[796,8,27]] two-graft planar tile-code reduction

Direction and hypothesis

The weight-8, local-2d-single CSS headline is [[798,8,d≤27]] in codes/798-8-27.json by @dorakingx, with kd²/n = 8 × 27² / 798 = 7.308. Two independent qubit reductions raise the witnessed score to 8 × 27² / 796 = 7.327, provided a lighter logical is not found.

Construction

All row and qubit indices here refer to the source codes/798-8-27.json. The first X-side row-space stabilizer is the XOR of rows 360, 376, 377, and 378. It has support S1={360,361,378,762,781,782}. Replace row 376 with S1, use S1 to clear qubit 378 from other X checks, apply CNOTs from qubit 378 to every other qubit in S1, then delete the disentangled qubit 378 and its weight-one check.

The second X-side stabilizer is the XOR of source rows 0, 1, 18, and 19. It has support S2={1,3,21,22,399,400,418,420} and is disjoint from S1. After the first deletion, source qubit 399 has index 398. Replace source row 0 with S2, clear that qubit from other X checks, apply the corresponding CNOT fanout, and delete the second disentangled qubit and weight-one check. Every surviving qubit keeps its source coordinate.

The final matrices are reproduced by this sequence. The repository verifier computes n=796, k=8, CSS commutation, maximum check weight 8, a connected stabilizer group, one layer, and interaction radius 4. The submitted X-27 and Z-27 logical witnesses validate on the full matrices. The X witness is transported from the source code; the Z witness is transported from the GPU-found Z-27 logical on the intermediate [[797,8,d≤27]] code in PR #3385. d≤27 is an upper bound, not a proof of exact distance.

Search and checks

The unchanged verify/validate_candidate.py gate passed against the clean board with seed 1110336512. It found no exact or Weisfeiler–Leman-equivalent board entry and marked the code as advancing through lower n.

The general accelerated RIS search found no logical below 27 in one million trials at pair depth 256, nor in 500,000 trials at pair depth 512. Five independent pure-Python searches at 8,000 trials each found weights 29, 30, 29, 27, and 31. These searches can refute a distance claim but do not establish a lower bound.

Attribution

The source tile code and its original logical witnesses belong to @dorakingx. GPT-6 (Codex), run as a single Codex agent for @vprusso, found and validated the two four-check row-space grafts, retaining the source coordinates and crediting the first reduction in PR #3385.

Parity checks

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