[[576,28,24]] · QEC Challenge

[[576,28,24]] d ≤

576

kd²/n

28.0

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 24, d_Z ≤ 24 · w_X = 9, w_Z = 9 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 24 · witness weight 24 (claimed upper_bound)

witness operator (support, 24 qubits)

[45, 46, 47, 150, 151, 155, 225, 226, 227, 331, 332, 333, 366, 367, 371, 438, 440, 442, 511, 512, 513, 546, 548, 550]

d_Z 24 · witness weight 24 (claimed upper_bound)

witness operator (support, 24 qubits)

[30, 34, 35, 104, 105, 106, 246, 247, 248, 282, 283, 284, 390, 394, 395, 427, 429, 431, 463, 465, 467, 536, 537, 538]

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 9 · H_Z 9

qubit degrees H_X 2–8 (mean 4.5) · H_Z 2–8 (mean 4.5)

trapping sets H_X (1,2)×96 (2,3)×192 (3,3)×96 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,2): 96 (1,3): 96 (1,4): 192 (1,6): 96 (1,8): 96 (2,3): 192 (2,4): 592 (2,5): 960 (2,6): 1248 (2,7): 224 (2,8): 2152 (2,9): 704 (2,10): 1264 (2,12): 992 (2,14): 192 (3,3): 96 (3,4): 896 (3,5): 3872 (3,6): 7232 (3,7): 11584 (3,8): 19032 (3,9): 18320 (3,10): 34752 (3,11): 17168 (3,12): 37740 (3,13): 10960 (3,14): 30272 (3,15): 4256 (3,16): 13896 (3,17): 160 (3,18): 4864 (3,20): 384

trapping sets H_Z (1,2)×96 (2,3)×192 (3,3)×96 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,2): 96 (1,3): 96 (1,4): 192 (1,6): 96 (1,8): 96 (2,3): 192 (2,4): 576 (2,5): 960 (2,6): 1296 (2,7): 224 (2,8): 2136 (2,9): 704 (2,10): 1232 (2,12): 1000 (2,14): 176 (3,3): 96 (3,4): 864 (3,5): 3812 (3,6): 7300 (3,7): 11860 (3,8): 19368 (3,9): 18160 (3,10): 34600 (3,11): 16944 (3,12): 37552 (3,13): 10976 (3,14): 29440 (3,15): 4080 (3,16): 13344 (3,17): 144 (3,18): 4576 (3,20): 336

Construction & provenance

authors @MathysRennela

provenance submitted through the challenge

novelty known parameter set; see provenance notes

construction Quantum Tanner code on a left-right Cayley complex over C4rC4; A- and B-side local codes both [6,3,3] shortened Hamming; matrices verbatim from arXiv:2512.20532 auxiliary files.

model DeepSeek V4 Flash 0731 (claimed, not verified)

builds on arXiv:2512.20532

date 2026-08-21

notes Reproduction of a published quantum Tanner code from arXiv:2512.20532 (Table 1b). Parity-check matrices taken verbatim from the paper's auxiliary files. Distance is witness-backed upper_bound; the paper reports a QDistRnd upper bound.

family quantum Tanner (a tag, not a ranking)

locality unrestricted (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

[[576,28,24]] quantum Tanner code on C4rC4

Reproduction of a published quantum Tanner code from arXiv:2512.20532 (Leverrier, Rozendaal, Zemor, "Small quantum Tanner codes from left-right Cayley complexes"), Table 1b.

Direction & hypothesis

The paper searches for small quantum Tanner codes on left-right Cayley complexes that are competitive at moderate block length. With A- and B-side local codes both the [6,3,3] shortened Hamming code, the lift group C4rC4 yields a [[576,28,24]] code with weight-9 checks — the paper's headline instance with k > sqrt(n) and d = sqrt(n). This reproduction stages the authors' published parity-check matrices so the instance can be verified on the board.

What was searched

This is a reproduction of a published instance, not a new parameter search. The paper's search enumerated groups and local-code combinations and estimated distances with QDistRnd (3M trials for this instance). We take the parity-check matrices verbatim from the arXiv auxiliary files (633x633/HX_C4rC4_576_28_24.mtx, 633x633/HZ_C4rC4_576_28_24.mtx).

Evidence trail

The matrices were read from the authors' .mtx files and packaged through the repo's submit.make_submission, which recomputes n/k, asserts CSS commutation, and extracts a lightest-logical witness per side. The trusted gate (verify/validate_candidate.py) reports passed: true: it verifies the structure and witnesses, finds nothing lighter than d=24 in its refutation search, and is not a board duplicate. The paper reports d<=24 (QDistRnd upper bound); this record is witness-backed upper_bound, so the true distance may be lower.

Dead ends

None for this reproduction. The paper's own search notes that aggressive short-cycle minimization generally reduced distance, and that abelian lifts carry constant-distance logicals.

Tools

Model/harness: DeepSeek V4 Flash 0731 (Zed agent). Reproduction used the repo's research/kit (submit.make_submission) and the trusted gate verify/validate_candidate.py. No new constructor code was written; the matrices come from the published auxiliary files.

Reproduction

Download the arXiv e-print 2512.20532v1 and read 633x633/HX_C4rC4_576_28_24.mtx and 633x633/HZ_C4rC4_576_28_24.mtx (Matrix Market, columns = qubits, rows = stabilizer generators). The submitted JSON contains the resulting sparse checks and logical witnesses.

Parity checks

X-checks 288 (max weight 9) · Z-checks 288 (max weight 9)

H_X (288 checks, sparse supports)

[1, 2, 3, 25, 26, 27, 31, 32, 33] [0, 2, 4, 24, 26, 28, 30, 32, 34] [0, 1, 5, 24, 25, 29, 30, 31, 35] [7, 8, 9, 19, 20, 21, 31, 32, 33] [6, 8, 10, 18, 20, 22, 30, 32, 34] [6, 7, 11, 18, 19, 23, 30, 31, 35] [13, 14, 15, 19, 20, 21, 25, 26, 27] [12, 14, 16, 18, 20, 22, 24, 26, 28] [12, 13, 17, 18, 19, 23, 24, 25, 29] [37, 38, 39, 61, 62, 63, 67, 68, 69] [36, 38, 40, 60, 62, 64, 66, 68, 70] [36, 37, 41, 60, 61, 65, 66, 67, 71] [43, 44, 45, 55, 56, 57, 67, 68, 69] [42, 44, 46, 54, 56, 58, 66, 68, 70] [42, 43, 47, 54, 55, 59, 66, 67, 71] [49, 50, 51, 55, 56, 57, 61, 62, 63] [48, 50, 52, 54, 56, 58, 60, 62, 64] [48, 49, 53, 54, 55, 59, 60, 61, 65] [73, 74, 75, 97, 98, 99, 103, 104, 105] [72, 74, 76, 96, 98, 100, 102, 104, 106] [72, 73, 77, 96, 97, 101, 102, 103, 107] [79, 80, 81, 91, 92, 93, 103, 104, 105] [78, 80, 82, 90, 92, 94, 102, 104, 106] [78, 79, 83, 90, 91, 95, 102, 103, 107] [85, 86, 87, 91, 92, 93, 97, 98, 99] [84, 86, 88, 90, 92, 94, 96, 98, 100] [84, 85, 89, 90, 91, 95, 96, 97, 101] [109, 110, 111, 133, 134, 135, 139, 140, 141] [108, 110, 112, 132, 134, 136, 138, 140, 142] [108, 109, 113, 132, 133, 137, 138, 139, 143] [115, 116, 117, 127, 128, 129, 139, 140, 141] [114, 116, 118, 126, 128, 130, 138, 140, 142] [114, 115, 119, 126, 127, 131, 138, 139, 143] [121, 122, 123, 127, 128, 129, 133, 134, 135] [120, 122, 124, 126, 128, 130, 132, 134, 136] [120, 121, 125, 126, 127, 131, 132, 133, 137] [145, 146, 147, 169, 170, 171, 175, 176, 177] [144, 146, 148, 168, 170, 172, 174, 176, 178] [144, 145, 149, 168, 169, 173, 174, 175, 179] [151, 152, 153, 163, 164, 165, 175, 176, 177] [150, 152, 154, 162, 164, 166, 174, 176, 178] [150, 151, 155, 162, 163, 167, 174, 175, 179] [157, 158, 159, 163, 164, 165, 169, 170, 171] [156, 158, 160, 162, 164, 166, 168, 170, 172] [156, 157, 161, 162, 163, 167, 168, 169, 173] [181, 182, 183, 205, 206, 207, 211, 212, 213] [180, 182, 184, 204, 206, 208, 210, 212, 214] [180, 181, 185, 204, 205, 209, 210, 211, 215] [187, 188, 189, 199, 200, 201, 211, 212, 213] [186, 188, 190, 198, 200, 202, 210, 212, 214] [186, 187, 191, 198, 199, 203, 210, 211, 215] [193, 194, 195, 199, 200, 201, 205, 206, 207] [192, 194, 196, 198, 200, 202, 204, 206, 208] [192, 193, 197, 198, 199, 203, 204, 205, 209] [217, 218, 219, 241, 242, 243, 247, 248, 249] [216, 218, 220, 240, 242, 244, 246, 248, 250] [216, 217, 221, 240, 241, 245, 246, 247, 251] [223, 224, 225, 235, 236, 237, 247, 248, 249] [222, 224, 226, 234, 236, 238, 246, 248, 250] [222, 223, 227, 234, 235, 239, 246, 247, 251] [229, 230, 231, 235, 236, 237, 241, 242, 243] [228, 230, 232, 234, 236, 238, 240, 242, 244] [228, 229, 233, 234, 235, 239, 240, 241, 245] [253, 254, 255, 277, 278, 279, 283, 284, 285] [252, 254, 256, 276, 278, 280, 282, 284, 286] [252, 253, 257, 276, 277, 281, 282, 283, 287] [259, 260, 261, 271, 272, 273, 283, 284, 285] [258, 260, 262, 270, 272, 274, 282, 284, 286] [258, 259, 263, 270, 271, 275, 282, 283, 287] [265, 266, 267, 271, 272, 273, 277, 278, 279] [264, 266, 268, 270, 272, 274, 276, 278, 280] [264, 265, 269, 270, 271, 275, 276, 277, 281] [289, 290, 291, 313, 314, 315, 319, 320, 321] [288, 290, 292, 312, 314, 316, 318, 320, 322] [288, 289, 293, 312, 313, 317, 318, 319, 323] [295, 296, 297, 307, 308, 309, 319, 320, 321] [294, 296, 298, 306, 308, 310, 318, 320, 322] [294, 295, 299, 306, 307, 311, 318, 319, 323] [301, 302, 303, 307, 308, 309, 313, 314, 315] [300, 302, 304, 306, 308, 310, 312, 314, 316] [300, 301, 305, 306, 307, 311, 312, 313, 317] [325, 326, 327, 349, 350, 351, 355, 356, 357] [324, 326, 328, 348, 350, 352, 354, 356, 358] [324, 325, 329, 348, 349, 353, 354, 355, 359] [331, 332, 333, 343, 344, 345, 355, 356, 357] [330, 332, 334, 342, 344, 346, 354, 356, 358] [330, 331, 335, 342, 343, 347, 354, 355, 359] [337, 338, 339, 343, 344, 345, 349, 350, 351] [336, 338, 340, 342, 344, 346, 348, 350, 352] [336, 337, 341, 342, 343, 347, 348, 349, 353] [361, 362, 363, 385, 386, 387, 391, 392, 393] [360, 362, 364, 384, 386, 388, 390, 392, 394] [360, 361, 365, 384, 385, 389, 390, 391, 395] [367, 368, 369, 379, 380, 381, 391, 392, 393] [366, 368, 370, 378, 380, 382, 390, 392, 394] [366, 367, 371, 378, 379, 383, 390, 391, 395] [373, 374, 375, 379, 380, 381, 385, 386, 387] [372, 374, 376, 378, 380, 382, 384, 386, 388] [372, 373, 377, 378, 379, 383, 384, 385, 389] [397, 398, 399, 421, 422, 423, 427, 428, 429] [396, 398, 400, 420, 422, 424, 426, 428, 430] [396, 397, 401, 420, 421, 425, 426, 427, 431] [403, 404, 405, 415, 416, 417, 427, 428, 429] [402, 404, 406, 414, 416, 418, 426, 428, 430] [402, 403, 407, 414, 415, 419, 426, 427, 431] [409, 410, 411, 415, 416, 417, 421, 422, 423] [408, 410, 412, 414, 416, 418, 420, 422, 424] [408, 409, 413, 414, 415, 419, 420, 421, 425] [433, 434, 435, 457, 458, 459, 463, 464, 465] [432, 434, 436, 456, 458, 460, 462, 464, 466] [432, 433, 437, 456, 457, 461, 462, 463, 467] [439, 440, 441, 451, 452, 453, 463, 464, 465] [438, 440, 442, 450, 452, 454, 462, 464, 466] [438, 439, 443, 450, 451, 455, 462, 463, 467] [445, 446, 447, 451, 452, 453, 457, 458, 459] [444, 446, 448, 450, 452, 454, 456, 458, 460] [444, 445, 449, 450, 451, 455, 456, 457, 461] [469, 470, 471, 493, 494, 495, 499, 500, 501] [468, 470, 472, 492, 494, 496, 498, 500, 502] [468, 469, 473, 492, 493, 497, 498, 499, 503] [475, 476, 477, 487, 488, 489, 499, 500, 501] [474, 476, 478, 486, 488, 490, 498, 500, 502] [474, 475, 479, 486, 487, 491, 498, 499, 503] [481, 482, 483, 487, 488, 489, 493, 494, 495] [480, 482, 484, 486, 488, 490, 492, 494, 496] [480, 481, 485, 486, 487, 491, 492, 493, 497] [505, 506, 507, 529, 530, 531, 535, 536, 537] [504, 506, 508, 528, 530, 532, 534, 536, 538] [504, 505, 509, 528, 529, 533, 534, 535, 539] [511, 512, 513, 523, 524, 525, 535, 536, 537] [510, 512, 514, 522, 524, 526, 534, 536, 538] [510, 511, 515, 522, 523, 527, 534, 535, 539] [517, 518, 519, 523, 524, 525, 529, 530, 531] [516, 518, 520, 522, 524, 526, 528, 530, 532] [516, 517, 521, 522, 523, 527, 528, 529, 533] [541, 542, 543, 565, 566, 567, 571, 572, 573] [540, 542, 544, 564, 566, 568, 570, 572, 574] [540, 541, 545, 564, 565, 569, 570, 571, 575] [547, 548, 549, 559, 560, 561, 571, 572, 573] [546, 548, 550, 558, 560, 562, 570, 572, 574] [546, 547, 551, 558, 559, 563, 570, 571, 575] [553, 554, 555, 559, 560, 561, 565, 566, 567] [552, 554, 556, 558, 560, 562, 564, 566, 568] [552, 553, 557, 558, 559, 563, 564, 565, 569] [3, 37, 98, 158, 171, 193, 277, 303, 326] [24, 98, 144, 158, 220, 326, 412, 496, 516] [24, 37, 125, 144, 193, 277, 293, 516, 533] [7, 129, 158, 188, 193, 235, 261, 303, 524] [42, 58, 118, 158, 188, 378, 412, 516, 524] [7, 42, 95, 125, 193, 235, 378, 516, 551] [98, 129, 140, 171, 235, 277, 357, 524, 571] [24, 58, 98, 102, 140, 378, 466, 496, 524] [24, 95, 102, 179, 235, 277, 378, 533, 571] [25, 39, 145, 195, 206, 279, 434, 482, 517] [60, 136, 206, 252, 340, 364, 434, 444, 482] [25, 53, 60, 145, 252, 401, 444, 517, 569] [9, 43, 195, 237, 332, 379, 482, 517, 560] [150, 166, 226, 332, 340, 444, 482, 486, 560] [43, 53, 150, 203, 299, 379, 444, 486, 517] [25, 68, 103, 206, 237, 279, 379, 560, 573] [60, 68, 136, 166, 206, 322, 426, 486, 560] [25, 60, 103, 203, 379, 426, 486, 503, 569] [26, 123, 146, 181, 229, 291, 457, 518, 531] [26, 52, 146, 312, 372, 400, 504, 518, 568] [89, 113, 181, 229, 312, 372, 389, 457, 504] [44, 79, 93, 123, 229, 380, 415, 518, 549] [44, 52, 202, 298, 342, 372, 380, 402, 518] [23, 79, 89, 229, 342, 372, 402, 415, 479] [26, 93, 104, 177, 283, 380, 415, 457, 531] [26, 30, 104, 202, 312, 342, 380, 502, 568] [23, 30, 283, 312, 342, 389, 415, 457, 539] [87, 111, 217, 314, 374, 387, 409, 493, 506] [40, 132, 196, 280, 314, 336, 360, 374, 506] [17, 77, 132, 217, 336, 353, 360, 409, 493] [21, 55, 87, 115, 344, 374, 404, 409, 477] [10, 162, 196, 222, 238, 336, 344, 374, 404] [17, 55, 115, 162, 222, 311, 336, 409, 443] [21, 32, 55, 314, 344, 387, 463, 493, 537] [32, 132, 162, 238, 280, 314, 318, 344, 574] [55, 132, 162, 311, 318, 353, 395, 463, 493] [14, 27, 61, 74, 147, 253, 350, 445, 519] [0, 14, 74, 168, 244, 300, 350, 472, 556] [0, 61, 168, 253, 300, 317, 377, 445, 509] [14, 45, 151, 308, 381, 440, 445, 487, 519] [14, 126, 258, 274, 300, 308, 370, 440, 556] [126, 151, 258, 300, 347, 377, 407, 445, 487] [27, 61, 105, 308, 350, 381, 392, 427, 487] [126, 168, 214, 244, 274, 308, 350, 354, 392] [35, 61, 126, 168, 317, 347, 354, 427, 487] [51, 62, 97, 157, 254, 325, 399, 446, 567] [62, 254, 264, 316, 376, 420, 446, 508, 540] [97, 157, 221, 264, 325, 413, 420, 497, 540] [51, 152, 157, 187, 201, 297, 446, 488, 523] [152, 264, 346, 376, 406, 446, 450, 488, 510] [59, 119, 157, 187, 264, 413, 450, 510, 523] [62, 97, 139, 201, 428, 488, 501, 523, 567] [34, 62, 246, 316, 346, 420, 428, 450, 488] [59, 97, 139, 246, 420, 450, 467, 497, 523] [133, 219, 266, 337, 361, 411, 422, 495, 542] [28, 148, 240, 266, 422, 468, 520, 542, 552] [133, 185, 233, 240, 337, 361, 461, 468, 552] [57, 117, 163, 223, 266, 337, 411, 452, 512] [46, 266, 270, 366, 382, 452, 512, 520, 552] [83, 163, 223, 233, 270, 337, 366, 419, 552] [57, 133, 163, 248, 319, 422, 452, 465, 495] [28, 106, 210, 240, 248, 270, 382, 422, 452] [133, 163, 210, 240, 270, 287, 319, 419, 461] [1, 63, 169, 182, 230, 255, 301, 447, 458] [36, 88, 112, 182, 192, 230, 276, 388, 458] [1, 36, 169, 192, 269, 276, 301, 425, 545] [80, 127, 153, 230, 259, 301, 416, 447, 489] [6, 22, 80, 88, 192, 230, 234, 416, 478] [6, 127, 192, 234, 259, 269, 301, 455, 515] [63, 127, 169, 284, 355, 416, 429, 458, 489] [22, 234, 276, 284, 388, 416, 458, 538, 570] [127, 169, 234, 251, 276, 355, 425, 455, 570] [15, 49, 75, 134, 338, 351, 362, 397, 565] [96, 134, 156, 184, 232, 324, 338, 362, 460] [5, 49, 96, 156, 173, 305, 324, 397, 565] [15, 49, 164, 199, 224, 295, 309, 338, 441] [82, 156, 164, 186, 224, 232, 338, 418, 522] [49, 131, 156, 186, 199, 263, 295, 305, 522] [134, 164, 199, 309, 320, 351, 393, 499, 565] [96, 134, 138, 164, 286, 320, 418, 460, 522] [96, 131, 138, 173, 199, 359, 499, 522, 565] [2, 170, 205, 302, 315, 375, 433, 481, 507] [2, 120, 170, 268, 288, 302, 424, 528, 544] [120, 137, 205, 288, 341, 365, 433, 481, 528] [128, 260, 302, 331, 345, 375, 405, 481, 559] [90, 120, 128, 260, 268, 302, 454, 514, 546] [90, 120, 167, 227, 331, 341, 481, 546, 559] [33, 67, 128, 170, 205, 315, 345, 356, 559] [90, 128, 170, 174, 250, 356, 424, 454, 528] [67, 90, 137, 167, 174, 205, 323, 528, 559] [122, 135, 241, 290, 339, 363, 469, 530, 553] [64, 84, 108, 122, 256, 290, 384, 448, 530] [84, 101, 108, 161, 241, 329, 384, 469, 553] [92, 122, 165, 225, 271, 339, 367, 548, 553] [18, 84, 92, 122, 154, 448, 474, 490, 548] [18, 84, 161, 191, 271, 367, 474, 527, 553] [92, 135, 165, 176, 211, 241, 271, 321, 530] [18, 64, 92, 176, 384, 430, 490, 530, 534] [18, 101, 143, 211, 241, 271, 384, 527, 534] [183, 231, 242, 313, 373, 459, 470, 505, 554] [100, 160, 204, 242, 328, 432, 470, 480, 554] [41, 197, 204, 281, 313, 373, 432, 480, 505] [81, 231, 272, 343, 368, 373, 403, 417, 554] [160, 190, 272, 330, 368, 480, 526, 554, 558] [11, 197, 239, 330, 343, 373, 403, 480, 558] [31, 212, 242, 272, 285, 313, 343, 417, 459] [66, 100, 142, 204, 212, 242, 272, 526, 558] [31, 66, 204, 239, 281, 313, 343, 558, 575] [13, 38, 73, 194, 267, 278, 349, 423, 543] [38, 48, 124, 194, 278, 292, 396, 532, 564] [13, 48, 73, 245, 349, 396, 473, 557, 564] [8, 13, 194, 236, 267, 307, 439, 453, 513] [8, 48, 94, 124, 194, 198, 236, 294, 550] [13, 48, 198, 275, 294, 307, 371, 439, 557] [236, 249, 278, 307, 349, 391, 423, 453, 572] [94, 178, 198, 236, 278, 498, 532, 564, 572] [198, 215, 245, 275, 307, 349, 391, 498, 564] [50, 85, 109, 243, 385, 398, 471, 555, 566] [4, 50, 172, 216, 304, 398, 408, 492, 566] [85, 109, 209, 216, 385, 408, 437, 485, 492] [19, 50, 85, 200, 273, 296, 369, 475, 555] [50, 54, 114, 130, 200, 262, 296, 304, 408] [19, 54, 85, 114, 335, 408, 475, 485, 563] [19, 200, 213, 243, 273, 385, 500, 535, 566] [54, 130, 172, 200, 358, 462, 492, 500, 566] [19, 54, 71, 209, 385, 462, 492, 535, 563] [86, 99, 110, 159, 265, 327, 386, 421, 541] [12, 72, 86, 110, 208, 348, 386, 436, 484] [12, 29, 72, 149, 265, 348, 421, 521, 541] [20, 86, 159, 189, 265, 451, 476, 511, 525] [12, 20, 86, 306, 334, 438, 476, 484, 562] [12, 47, 265, 306, 383, 438, 451, 511, 521] [20, 99, 141, 247, 386, 421, 451, 525, 536] [20, 70, 208, 306, 348, 386, 390, 536, 562] [29, 107, 247, 306, 348, 383, 390, 421, 451] [121, 207, 218, 289, 410, 435, 483, 494, 529] [16, 76, 180, 218, 228, 352, 410, 456, 494] [65, 121, 180, 228, 257, 289, 449, 456, 529] [56, 91, 116, 121, 333, 410, 483, 547, 561] [16, 56, 78, 116, 228, 310, 410, 414, 442] [78, 91, 121, 155, 228, 414, 449, 491, 547] [56, 69, 91, 175, 207, 464, 494, 529, 561] [56, 282, 310, 352, 394, 414, 456, 464, 494] [65, 91, 175, 282, 414, 431, 456, 491, 529]

H_Z (288 checks, sparse supports)

[150, 154, 155, 426, 430, 431, 486, 490, 491] [151, 153, 155, 427, 429, 431, 487, 489, 491] [152, 153, 154, 428, 429, 430, 488, 489, 490] [60, 64, 65, 252, 256, 257, 426, 430, 431] [61, 63, 65, 253, 255, 257, 427, 429, 431] [62, 63, 64, 254, 255, 256, 428, 429, 430] [150, 154, 155, 252, 256, 257, 444, 448, 449] [151, 153, 155, 253, 255, 257, 445, 447, 449] [152, 153, 154, 254, 255, 256, 446, 447, 448] [126, 130, 131, 258, 262, 263, 354, 358, 359] [127, 129, 131, 259, 261, 263, 355, 357, 359] [128, 129, 130, 260, 261, 262, 356, 357, 358] [0, 4, 5, 168, 172, 173, 354, 358, 359] [1, 3, 5, 169, 171, 173, 355, 357, 359] [2, 3, 4, 170, 171, 172, 356, 357, 358] [0, 4, 5, 258, 262, 263, 300, 304, 305] [1, 3, 5, 259, 261, 263, 301, 303, 305] [2, 3, 4, 260, 261, 262, 302, 303, 304] [66, 70, 71, 330, 334, 335, 558, 562, 563] [67, 69, 71, 331, 333, 335, 559, 561, 563] [68, 69, 70, 332, 333, 334, 560, 561, 562] [66, 70, 71, 204, 208, 209, 432, 436, 437] [67, 69, 71, 205, 207, 209, 433, 435, 437] [68, 69, 70, 206, 207, 208, 434, 435, 436] [330, 334, 335, 432, 436, 437, 480, 484, 485] [331, 333, 335, 433, 435, 437, 481, 483, 485] [332, 333, 334, 434, 435, 436, 482, 483, 484] [210, 214, 215, 270, 274, 275, 366, 370, 371] [211, 213, 215, 271, 273, 275, 367, 369, 371] [212, 213, 214, 272, 273, 274, 368, 369, 370] [210, 214, 215, 240, 244, 245, 468, 472, 473] [211, 213, 215, 241, 243, 245, 469, 471, 473] [212, 213, 214, 242, 243, 244, 470, 471, 472] [366, 370, 371, 468, 472, 473, 552, 556, 557] [367, 369, 371, 469, 471, 473, 553, 555, 557] [368, 369, 370, 470, 471, 472, 554, 555, 556] [6, 10, 11, 234, 238, 239, 570, 574, 575] [7, 9, 11, 235, 237, 239, 571, 573, 575] [8, 9, 10, 236, 237, 238, 572, 573, 574] [36, 40, 41, 276, 280, 281, 570, 574, 575] [37, 39, 41, 277, 279, 281, 571, 573, 575] [38, 39, 40, 278, 279, 280, 572, 573, 574] [6, 10, 11, 36, 40, 41, 192, 196, 197] [7, 9, 11, 37, 39, 41, 193, 195, 197] [8, 9, 10, 38, 39, 40, 194, 195, 196] [306, 310, 311, 390, 394, 395, 438, 442, 443] [307, 309, 311, 391, 393, 395, 439, 441, 443] [308, 309, 310, 392, 393, 394, 440, 441, 442] [72, 76, 77, 348, 352, 353, 390, 394, 395] [73, 75, 77, 349, 351, 353, 391, 393, 395] [74, 75, 76, 350, 351, 352, 392, 393, 394] [12, 16, 17, 72, 76, 77, 438, 442, 443] [13, 15, 17, 73, 75, 77, 439, 441, 443] [14, 15, 16, 74, 75, 76, 440, 441, 442] [18, 22, 23, 474, 478, 479, 534, 538, 539] [19, 21, 23, 475, 477, 479, 535, 537, 539] [20, 21, 22, 476, 477, 478, 536, 537, 538] [108, 112, 113, 384, 388, 389, 534, 538, 539] [109, 111, 113, 385, 387, 389, 535, 537, 539] [110, 111, 112, 386, 387, 388, 536, 537, 538] [84, 88, 89, 108, 112, 113, 474, 478, 479] [85, 87, 89, 109, 111, 113, 475, 477, 479] [86, 87, 88, 110, 111, 112, 476, 477, 478] [42, 46, 47, 102, 106, 107, 378, 382, 383] [43, 45, 47, 103, 105, 107, 379, 381, 383] [44, 45, 46, 104, 105, 106, 380, 381, 382] [24, 28, 29, 102, 106, 107, 144, 148, 149] [25, 27, 29, 103, 105, 107, 145, 147, 149] [26, 27, 28, 104, 105, 106, 146, 147, 148] [42, 46, 47, 144, 148, 149, 516, 520, 521] [43, 45, 47, 145, 147, 149, 517, 519, 521] [44, 45, 46, 146, 147, 148, 518, 519, 520] [246, 250, 251, 450, 454, 455, 510, 514, 515] [247, 249, 251, 451, 453, 455, 511, 513, 515] [248, 249, 250, 452, 453, 454, 512, 513, 514] [246, 250, 251, 420, 424, 425, 540, 544, 545] [247, 249, 251, 421, 423, 425, 541, 543, 545] [248, 249, 250, 422, 423, 424, 542, 543, 544] [264, 268, 269, 510, 514, 515, 540, 544, 545] [265, 267, 269, 511, 513, 515, 541, 543, 545] [266, 267, 268, 512, 513, 514, 542, 543, 544] [78, 82, 83, 282, 286, 287, 414, 418, 419] [79, 81, 83, 283, 285, 287, 415, 417, 419] [80, 81, 82, 284, 285, 286, 416, 417, 418] [180, 184, 185, 282, 286, 287, 456, 460, 461] [181, 183, 185, 283, 285, 287, 457, 459, 461] [182, 183, 184, 284, 285, 286, 458, 459, 460] [78, 82, 83, 180, 184, 185, 228, 232, 233] [79, 81, 83, 181, 183, 185, 229, 231, 233] [80, 81, 82, 182, 183, 184, 230, 231, 232] [54, 58, 59, 114, 118, 119, 462, 466, 467] [55, 57, 59, 115, 117, 119, 463, 465, 467] [56, 57, 58, 116, 117, 118, 464, 465, 466] [216, 220, 221, 462, 466, 467, 492, 496, 497] [217, 219, 221, 463, 465, 467, 493, 495, 497] [218, 219, 220, 464, 465, 466, 494, 495, 496] [114, 118, 119, 216, 220, 221, 408, 412, 413] [115, 117, 119, 217, 219, 221, 409, 411, 413] [116, 117, 118, 218, 219, 220, 410, 411, 412] [90, 94, 95, 174, 178, 179, 546, 550, 551] [91, 93, 95, 175, 177, 179, 547, 549, 551] [92, 93, 94, 176, 177, 178, 548, 549, 550] [174, 178, 179, 288, 292, 293, 528, 532, 533] [175, 177, 179, 289, 291, 293, 529, 531, 533] [176, 177, 178, 290, 291, 292, 530, 531, 532] [120, 124, 125, 288, 292, 293, 546, 550, 551] [121, 123, 125, 289, 291, 293, 547, 549, 551] [122, 123, 124, 290, 291, 292, 548, 549, 550] [138, 142, 143, 186, 190, 191, 522, 526, 527] [139, 141, 143, 187, 189, 191, 523, 525, 527] [140, 141, 142, 188, 189, 190, 524, 525, 526] [96, 100, 101, 138, 142, 143, 324, 328, 329] [97, 99, 101, 139, 141, 143, 325, 327, 329] [98, 99, 100, 140, 141, 142, 326, 327, 328] [156, 160, 161, 186, 190, 191, 324, 328, 329] [157, 159, 161, 187, 189, 191, 325, 327, 329] [158, 159, 160, 188, 189, 190, 326, 327, 328] [162, 166, 167, 222, 226, 227, 318, 322, 323] [163, 165, 167, 223, 225, 227, 319, 321, 323] [164, 165, 166, 224, 225, 226, 320, 321, 322] [132, 136, 137, 318, 322, 323, 360, 364, 365] [133, 135, 137, 319, 321, 323, 361, 363, 365] [134, 135, 136, 320, 321, 322, 362, 363, 364] [222, 226, 227, 336, 340, 341, 360, 364, 365] [223, 225, 227, 337, 339, 341, 361, 363, 365] [224, 225, 226, 338, 339, 340, 362, 363, 364] [198, 202, 203, 294, 298, 299, 498, 502, 503] [199, 201, 203, 295, 297, 299, 499, 501, 503] [200, 201, 202, 296, 297, 298, 500, 501, 502] [396, 400, 401, 498, 502, 503, 564, 568, 569] [397, 399, 401, 499, 501, 503, 565, 567, 569] [398, 399, 400, 500, 501, 502, 566, 567, 568] [48, 52, 53, 294, 298, 299, 396, 400, 401] [49, 51, 53, 295, 297, 299, 397, 399, 401] [50, 51, 52, 296, 297, 298, 398, 399, 400] [30, 34, 35, 342, 346, 347, 402, 406, 407] [31, 33, 35, 343, 345, 347, 403, 405, 407] [32, 33, 34, 344, 345, 346, 404, 405, 406] [30, 34, 35, 312, 316, 317, 504, 508, 509] [31, 33, 35, 313, 315, 317, 505, 507, 509] [32, 33, 34, 314, 315, 316, 506, 507, 508] [372, 376, 377, 402, 406, 407, 504, 508, 509] [373, 375, 377, 403, 405, 407, 505, 507, 509] [374, 375, 376, 404, 405, 406, 506, 507, 508] [258, 264, 270, 370, 376, 382, 407, 413, 419] [45, 51, 57, 151, 157, 163, 407, 413, 419] [45, 51, 57, 370, 376, 382, 440, 446, 452] [252, 264, 276, 364, 376, 388, 401, 413, 425] [39, 51, 63, 145, 157, 169, 401, 413, 425] [39, 51, 63, 364, 376, 388, 434, 446, 458] [252, 258, 282, 364, 370, 394, 401, 407, 431] [39, 45, 69, 145, 151, 175, 401, 407, 431] [39, 45, 69, 364, 370, 394, 434, 440, 464] [6, 12, 18, 478, 484, 490, 515, 521, 527] [153, 159, 165, 259, 265, 271, 515, 521, 527] [80, 86, 92, 153, 159, 165, 478, 484, 490] [0, 12, 24, 472, 484, 496, 509, 521, 533] [147, 159, 171, 253, 265, 277, 509, 521, 533] [74, 86, 98, 147, 159, 171, 472, 484, 496] [0, 6, 30, 472, 478, 502, 509, 515, 539] [147, 153, 177, 253, 259, 283, 509, 515, 539] [74, 80, 104, 147, 153, 177, 472, 478, 502] [227, 233, 239, 514, 520, 526, 546, 552, 558] [227, 233, 239, 331, 337, 343, 405, 411, 417] [260, 266, 272, 405, 411, 417, 514, 520, 526] [221, 233, 245, 508, 520, 532, 540, 552, 564] [221, 233, 245, 325, 337, 349, 399, 411, 423] [254, 266, 278, 399, 411, 423, 508, 520, 532] [221, 227, 251, 508, 514, 538, 540, 546, 570] [221, 227, 251, 325, 331, 355, 399, 405, 429] [254, 260, 284, 399, 405, 429, 508, 514, 538] [154, 160, 166, 191, 197, 203, 474, 480, 486] [191, 197, 203, 225, 231, 237, 367, 373, 379] [154, 160, 166, 225, 231, 237, 548, 554, 560] [148, 160, 172, 185, 197, 209, 468, 480, 492] [185, 197, 209, 219, 231, 243, 361, 373, 385] [148, 160, 172, 219, 231, 243, 542, 554, 566] [148, 154, 178, 185, 191, 215, 468, 474, 498] [185, 191, 215, 219, 225, 249, 361, 367, 391] [148, 154, 178, 219, 225, 249, 542, 548, 572] [42, 48, 54, 118, 124, 130, 551, 557, 563] [7, 13, 19, 261, 267, 273, 551, 557, 563] [118, 124, 130, 188, 194, 200, 261, 267, 273] [36, 48, 60, 112, 124, 136, 545, 557, 569] [1, 13, 25, 255, 267, 279, 545, 557, 569] [112, 124, 136, 182, 194, 206, 255, 267, 279] [36, 42, 66, 112, 118, 142, 545, 551, 575] [1, 7, 31, 255, 261, 285, 545, 551, 575] [112, 118, 142, 182, 188, 212, 255, 261, 285] [294, 300, 306, 371, 377, 383, 550, 556, 562] [371, 377, 383, 439, 445, 451, 513, 519, 525] [8, 14, 20, 513, 519, 525, 550, 556, 562] [288, 300, 312, 365, 377, 389, 544, 556, 568] [365, 377, 389, 433, 445, 457, 507, 519, 531] [2, 14, 26, 507, 519, 531, 544, 556, 568] [288, 294, 318, 365, 371, 395, 544, 550, 574] [365, 371, 395, 433, 439, 463, 507, 513, 537] [2, 8, 32, 507, 513, 537, 544, 550, 574] [114, 120, 126, 262, 268, 274, 335, 341, 347] [335, 341, 347, 369, 375, 381, 475, 481, 487] [262, 268, 274, 296, 302, 308, 369, 375, 381] [108, 120, 132, 256, 268, 280, 329, 341, 353] [329, 341, 353, 363, 375, 387, 469, 481, 493] [256, 268, 280, 290, 302, 314, 363, 375, 387] [108, 114, 138, 256, 262, 286, 329, 335, 359] [329, 335, 359, 363, 369, 393, 469, 475, 499] [256, 262, 286, 290, 296, 320, 363, 369, 393] [150, 156, 162, 226, 232, 238, 299, 305, 311] [9, 15, 21, 43, 49, 55, 299, 305, 311] [9, 15, 21, 226, 232, 238, 332, 338, 344] [144, 156, 168, 220, 232, 244, 293, 305, 317] [3, 15, 27, 37, 49, 61, 293, 305, 317] [3, 15, 27, 220, 232, 244, 326, 338, 350] [144, 150, 174, 220, 226, 250, 293, 299, 323] [3, 9, 33, 37, 43, 67, 293, 299, 323] [3, 9, 33, 220, 226, 250, 326, 332, 356] [47, 53, 59, 334, 340, 346, 438, 444, 450] [47, 53, 59, 189, 195, 201, 511, 517, 523] [189, 195, 201, 334, 340, 346, 476, 482, 488] [41, 53, 65, 328, 340, 352, 432, 444, 456] [41, 53, 65, 183, 195, 207, 505, 517, 529] [183, 195, 207, 328, 340, 352, 470, 482, 494] [41, 47, 71, 328, 334, 358, 432, 438, 462] [41, 47, 71, 183, 189, 213, 505, 511, 535] [183, 189, 213, 328, 334, 358, 470, 476, 500] [298, 304, 310, 402, 408, 414, 479, 485, 491] [79, 85, 91, 479, 485, 491, 549, 555, 561] [44, 50, 56, 298, 304, 310, 549, 555, 561] [292, 304, 316, 396, 408, 420, 473, 485, 497] [73, 85, 97, 473, 485, 497, 543, 555, 567] [38, 50, 62, 292, 304, 316, 543, 555, 567] [292, 298, 322, 396, 402, 426, 473, 479, 503] [73, 79, 103, 473, 479, 503, 543, 549, 573] [38, 44, 68, 292, 298, 322, 543, 549, 573] [10, 16, 22, 222, 228, 234, 443, 449, 455] [115, 121, 127, 443, 449, 455, 477, 483, 489] [10, 16, 22, 404, 410, 416, 477, 483, 489] [4, 16, 28, 216, 228, 240, 437, 449, 461] [109, 121, 133, 437, 449, 461, 471, 483, 495] [4, 16, 28, 398, 410, 422, 471, 483, 495] [4, 10, 34, 216, 222, 246, 437, 443, 467] [109, 115, 139, 437, 443, 467, 471, 477, 501] [4, 10, 34, 398, 404, 428, 471, 477, 501] [78, 84, 90, 155, 161, 167, 442, 448, 454] [155, 161, 167, 333, 339, 345, 547, 553, 559] [116, 122, 128, 333, 339, 345, 442, 448, 454] [72, 84, 96, 149, 161, 173, 436, 448, 460] [149, 161, 173, 327, 339, 351, 541, 553, 565] [110, 122, 134, 327, 339, 351, 436, 448, 460] [72, 78, 102, 149, 155, 179, 436, 442, 466] [149, 155, 179, 327, 333, 357, 541, 547, 571] [110, 116, 140, 327, 333, 357, 436, 442, 466] [119, 125, 131, 406, 412, 418, 510, 516, 522] [119, 125, 131, 187, 193, 199, 297, 303, 309] [152, 158, 164, 297, 303, 309, 406, 412, 418] [113, 125, 137, 400, 412, 424, 504, 516, 528] [113, 125, 137, 181, 193, 205, 291, 303, 315] [146, 158, 170, 291, 303, 315, 400, 412, 424] [113, 119, 143, 400, 406, 430, 504, 510, 534] [113, 119, 143, 181, 187, 211, 291, 297, 321] [146, 152, 176, 291, 297, 321, 400, 406, 430] [46, 52, 58, 83, 89, 95, 366, 372, 378] [83, 89, 95, 117, 123, 129, 223, 229, 235] [46, 52, 58, 117, 123, 129, 512, 518, 524] [40, 52, 64, 77, 89, 101, 360, 372, 384] [77, 89, 101, 111, 123, 135, 217, 229, 241] [40, 52, 64, 111, 123, 135, 506, 518, 530] [40, 46, 70, 77, 83, 107, 360, 366, 390] [77, 83, 107, 111, 117, 141, 217, 223, 247] [40, 46, 70, 111, 117, 141, 506, 512, 536] [82, 88, 94, 186, 192, 198, 263, 269, 275] [263, 269, 275, 295, 301, 307, 441, 447, 453] [82, 88, 94, 224, 230, 236, 441, 447, 453] [76, 88, 100, 180, 192, 204, 257, 269, 281] [257, 269, 281, 289, 301, 313, 435, 447, 459] [76, 88, 100, 218, 230, 242, 435, 447, 459] [76, 82, 106, 180, 186, 210, 257, 263, 287] [257, 263, 287, 289, 295, 319, 435, 441, 465] [76, 82, 106, 218, 224, 248, 435, 441, 465] [11, 17, 23, 190, 196, 202, 330, 336, 342] [11, 17, 23, 81, 87, 93, 403, 409, 415] [81, 87, 93, 190, 196, 202, 368, 374, 380] [5, 17, 29, 184, 196, 208, 324, 336, 348] [5, 17, 29, 75, 87, 99, 397, 409, 421] [75, 87, 99, 184, 196, 208, 362, 374, 386] [5, 11, 35, 184, 190, 214, 324, 330, 354] [5, 11, 35, 75, 81, 105, 397, 403, 427] [75, 81, 105, 184, 190, 214, 362, 368, 392]

Code ID 576-28-24 · download JSON · raw on GitHub