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[[709,8,25]] d ≤
n
709
k
8
d
25
kd²/n
7.052
w
8
X/Z
1
g
0.11
r
4.0
layers
1
swaps
1348

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Distance

X/Z asymmetry 1 · d_X ≤ 25, 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 25 · witness weight 25 (claimed upper_bound)
witness found by @vprusso · RIS on 719-qubit ancestor; projected through later pivots · found at 105 trials · 2026-10-16
witness operator (support, 25 qubits)
[1, 3, 6, 7, 8, 9, 22, 23, 30, 36, 37, 52, 357, 358, 362, 364, 376, 378, 384, 385, 386, 387, 392, 406, 447]
d_Z 25 · witness weight 25 (claimed upper_bound)
witness found by @fullymiddleaged and @vprusso · Inherited from codes/722-8-25.json via thirteen pivots · found at 1 trials · 2026-10-16
witness operator (support, 25 qubits)
[20, 21, 40, 59, 97, 172, 174, 191, 192, 193, 250, 270, 289, 310, 329, 359, 415, 453, 472, 489, 508, 547, 567, 681, 699]
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 7.207) · H_Z 2–8 (mean 7.261)
qubit degrees H_X 1–4 (mean 3.578) · H_Z 1–5 (mean 3.574)
trapping sets H_X (1,1)×39 (2,0)×4 (3,0)×32 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 39 (1,2): 70 (1,3): 42 (1,4): 558 (2,0): 4 (2,1): 112 (2,2): 192 (2,3): 374 (2,4): 1667 (2,5): 256 (2,6): 4353 (3,0): 32 (3,1): 184 (3,2): 620 (3,3): 1867 (3,4): 4820 (3,5): 5020 (3,6): 30254 (3,7): 3402 (3,8): 49962 (3,9): 139 (3,10): 3350
trapping sets H_Z (1,1)×58 (2,0)×21 (3,0)×16 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 58 (1,2): 38 (1,3): 53 (1,4): 559 (1,5): 1 (2,0): 21 (2,1): 91 (2,2): 176 (2,3): 380 (2,4): 1557 (2,5): 358 (2,6): 4354 (2,7): 7 (3,0): 16 (3,1): 184 (3,2): 702 (3,3): 1704 (3,4): 4289 (3,5): 5370 (3,6): 29255 (3,7): 4335 (3,8): 49918 (3,9): 313 (3,10): 3339 (3,11): 5
witness diameter X 24.8395 · 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 (709)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 1348 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 @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction From codes/722-8-25.json, successively pivot out: qubit 0 with Z row 289 support [0,362,363]; qubit 18 with Z row 289 support [1,18,361,380,381]; qubit 357 with Z row 350 support [356,357,716]; qubit 357 with Z row 353 support [356,357,715,716]; qubit 17 with X row 291 support [16,17,35,393,412,413]; qubit 341 with X row 272 support [301,302,321,341,662,679,698,699]; qubit 321 with X row 348 support [282,301,321,641,678]; qubit 341 with X row 273 support [303,304,322,341,662,679,698,699]; qubit 695 with Z row 290 support [339,695]; qubit 485 with Z row 84 support [90,91,110,127,445,465,484,485]; qubit 711 with Z row 287 support [318,319,337,352,672,692,710,711]; qubit 693 with X row 352 support [319,693]; qubit 674 with Z row 253 support [280,281,300,317,634,654,673,674]. At each step, XOR the pivot row into same-side checks containing the target, delete that row and qubit, shorten opposite-side checks, and remove the coordinate.
model GPT-6 (Codex) (claimed, not verified)
builds on arXiv:2504.09171
date 2026-10-16
notes X logical descends from RIS on the 719-qubit ancestor; Z logical descends from codes/722-8-25.json.
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

[[709,8,25]] — thirteen local reductions of a planar tile code

Direction & hypothesis

The published codes/722-8-25.json is a weight-8, single-layer 2D tile code with eight logical qubits and explicit weight-25 logical operators. Local stabilizer pivots can remove physical qubits while retaining its checks, layout class, and logical witnesses. We sought a smaller n in that board cell. The reported distance is a witness-backed upper bound.

What was searched

Twelve compatible pivots reduced the published 722-qubit code to a staged 710-qubit ancestor. A thirteenth single-pivot scan found 98 structural 709-qubit variants preserving check weight at most 8, radius at most 4, and inherited weight-25 logicals. Fifty-five retained k=8, Tanner and stabilizer-block connectivity, and valid logicals. Projection of 396 light ancestor logicals, including stabilizer-row translates and RIS witnesses lifted from the children, refuted 15 variants with lighter logicals. A 10,000-trial, pair-depth-8 screen covered all 51 initial survivors.

At 100,000 trials and pair depth 512, X692/pivot347 and X709/pivot286 returned weight 25; Z675/pivot287 produced a weight-24 X logical. X692/pivot347 passed shorter checks and the trusted gate, but both million-trial runs found the same weight-24 Z logical. The unchanged verifier confirmed those refutations. X675/pivot255, Z636/pivot219, and Z674/pivot253 each returned weight 25 at 100,000 pair-depth-512 trials. We selected Z674/pivot253 for the final code.

Evidence trail

The unchanged trusted candidate gate passed the Z674/pivot253 JSON with seed 806842242 against the 2026-10-17 board. It checked CSS commutation, n=709, k=8, maximum check weight 8, a connected one-layer radius-4 layout, the two weight-25 logicals, deduplication, and an 8,000-trial RIS refutation search. It marked the weight-8, local-2d-single cell as advancing by lower n. An independent thirteen-pivot reconstruction from codes/722-8-25.json matched the candidate checks and coordinates. The Z witness matches the published parent's projection; the X witness descends from a validated RIS result on the 719-qubit ancestor.

On the exact 709-qubit matrices, accelerated RIS returned no logical below 25 in 100,000 pair-depth-512 trials (seed 1221267653), 300,000 pair-depth-512 trials (seed 1221467653), 200,000 pair-depth-4096 trials (seed 4805367653), 1,000,000 pair-depth-512 trials (seed 1222167653), and 1,000,000 pair-depth-4096 trials (seed 4806167653). Every returned logical was checked against those matrices. The initial 10,000-trial pair-depth-8 run returned a weight-27 logical, while the candidate already contained valid weight-25 witnesses.

d≤25 is a witness-backed upper bound. The bounded searches do not prove a minimum distance of 25. The witnessed score is 8 × 25² / 709 = 7.052, versus 6.925 for the published parent. The current board also has codes/717-8-25.json; this code removes eight more physical qubits at the same k, witnessed bound, weight, and layout class.

Dead ends

X692/pivot347 fell to a trusted-verifier-confirmed weight-24 Z logical in both million-trial screens. Z390/pivot348 and Z675/pivot287 also had confirmed weight-24 logicals. Saved logical projections ruled out 15 variants in total. The other shallow-screen survivors have not been deeply confirmed.

Tools

GPT-6 (Codex) ran as one agent for @vprusso. The repository's unchanged verifier and candidate gate, exact GF(2) rank, connectivity routines, and accelerated gf2_fast RIS screened and checked candidates.

Reproduction

Start from codes/722-8-25.json. At each step, XOR the named pivot row into every other same-side check containing the target qubit; delete the pivot row and qubit, shorten opposite-side checks, delete that coordinate, and renumber surviving qubits. In order:

1. Z row 289, support {0,362,363}, target qubit 0. 2. Z row 289, support {1,18,361,380,381}, target qubit 18. 3. Z row 350, support {356,357,716}, target qubit 357. 4. Z row 353, support {356,357,715,716}, target qubit 357. 5. X row 291, support {16,17,35,393,412,413}, target qubit 17. 6. X row 272, support {301,302,321,341,662,679,698,699}, target qubit 341. 7. X row 348, support {282,301,321,641,678}, target qubit 321. 8. X row 273, support {303,304,322,341,662,679,698,699}, target qubit 341. 9. Z row 290, support {339,695}, target qubit 695. 10. Z row 84, support {90,91,110,127,445,465,484,485}, target qubit 485. 11. Z row 287, support {318,319,337,352,672,692,710,711}, target qubit 711. 12. X row 352, support {319,693}, target qubit 693. 13. Z row 253, support {280,281,300,317,634,654,673,674}, target qubit 674.

Project the published Z witness through all thirteen pivots. The X witness in the candidate JSON comes from accelerated RIS on the 719-qubit intermediate and is projected through the final ten pivots. The JSON contains the final checks, coordinates, and both witness supports.

Parity checks

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