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[[722,8,25]] d ≤
n
722
k
8
d
25
kd²/n
6.925
w
8
X/Z
1.04
g
0.108
r
4.0
layers
1
swaps
1377

Share this result

Distance

X/Z asymmetry 1.04 · d_X ≤ 26, d_Z ≤ 25 · 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 26 · witness weight 26 (claimed upper_bound)
witness operator (support, 26 qubits)
[4, 6, 7, 9, 10, 14, 16, 20, 24, 25, 26, 32, 367, 368, 370, 371, 373, 374, 375, 376, 379, 380, 383, 386, 391, 392]
d_Z 25 · witness weight 25 (claimed upper_bound)
witness operator (support, 25 qubits)
[23, 24, 43, 62, 100, 175, 177, 194, 195, 196, 253, 273, 292, 313, 333, 367, 423, 461, 480, 498, 517, 556, 576, 691, 711]
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 7.238) · H_Z 3–8 (mean 7.238)
qubit degrees H_X 1–4 (mean 3.579) · H_Z 1–4 (mean 3.579)
trapping sets H_X (1,1)×38 (2,1)×123 (3,0)×34 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 38 (1,2): 76 (1,3): 38 (1,4): 570 (2,1): 123 (2,2): 201 (2,3): 382 (2,4): 1716 (2,5): 215 (2,6): 4457 (3,0): 34 (3,1): 189 (3,2): 641 (3,3): 1967 (3,4): 4979 (3,5): 5000 (3,6): 31054 (3,7): 3005 (3,8): 51190 (3,9): 85 (3,10): 3441
trapping sets H_Z (1,1)×57 (2,0)×17 (3,0)×17 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 57 (1,2): 38 (1,3): 57 (1,4): 570 (2,0): 17 (2,1): 89 (2,2): 179 (2,3): 379 (2,4): 1583 (2,5): 376 (2,6): 4453 (3,0): 17 (3,1): 173 (3,2): 702 (3,3): 1685 (3,4): 4313 (3,5): 5465 (3,6): 29809 (3,7): 4468 (3,8): 51125 (3,9): 241 (3,10): 3433
witness diameter X 25.4951 · Z 25.6125 (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 (722)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 1377 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 @fullymiddleaged
provenance submitted through the challenge
novelty novelty not audited
construction Tile code (Steffan, Choe, Breuckmann, Pereira, Eberhardt, arXiv:2504.09171) with box B = 3 on a 17 x 17 bulk, open boundaries as in the paper; X-tile {h00,h01,h11,h22,v02,v10,v20,v21}, Z-tile by their condition T2: the tile of codes/288-8-15.json and codes/338-8-16.json. Single-layer layout: each edge on its own integer site of the 45-degree rotated lattice, interaction radius 4.000.
model Claude Claude Opus 5.5 (claimed, not verified)
date 2026-10-16
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

[[722,8,25]] — single-layer weight-8 tile code (3 x 3 tile, 17 x 17 bulk)

Direction & hypothesis

The X-tile {h00, h01, h11, h22, v02, v10, v20, v21} of codes/288-8-15.json and codes/338-8-16.json (ours) gains distance steadily with the bulk, and codes/800-8-27.json built it at 20 x 20. Between n = 338 and 796 the single-layer weight-8 cell at k = 8 held only weight-6 codes, so we built the tile at the sizes in between.

What was searched

  • The tile on square bulks 12 x 12 to 17 x 17 (n = 392 to 722), the paper's open boundary (Steffan, Choe, Breuckmann,

    • Pereira, Eberhardt, arXiv:2504.09171). On 17 x 17 it gives [[722,8,25]].

Evidence trail

  • Fresh-seed RIS ladder with this repository's bit-packed engine (verify/gf2_fast.cpp), each rung on its own seed:

    • 25 at 20k, 26 at 200k, 25 at 1M, 25 at 5M, 25 at 20M trials, nothing lighter. The distance is a witness-backed upper bound, not a proof.

  • Not dominated in weight-8 x local-2d-single: the best k = 8 entry at n <= 722 is codes/658-8-20.json (d 20, weight 6); the next entry

    • reaching d = 25 is codes/796-8-27.json (d 27).

Dead ends

  • We tried row-space grafts on the 12 x 12 to 14 x 14 bulks (notes/280-8-15.md describes the move); above n = 500 they mostly cost distance, so this size goes in ungrafted.
  • At n >= 578 the RIS bound kept falling with more trials (22 to 21 at n = 578, 24 to 23 at n = 648), so we report

    • the lightest logical found and treat larger budgets as able to lower it further.

Tools

Claude Opus 5.5 in Claude Code; our research package (tile construction, graft, RIS ladder); this repository's verify/gf2_fast.cpp (RIS), cli/qldpc.py and verify/.

Reproduction

B = 3, X-tile {h00, h01, h11, h22, v02, v10, v20, v21} where h(x, y) joins vertices (x, y) and (x + 1, y) and v(x, y) joins (x, y) and (x, y + 1); Z-tile by T2 (h(x, y) <-> v(2 - x, 2 - y)); the paper's boundary on a 17 x 17 bulk. The checks and the coordinates (one qubit per site of the 45-degree rotated lattice) are in the submission JSON.

Parity checks

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