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[[824,32,20]] d ≤
n
824
k
32
d
20
kd²/n
15.534
w
7
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 20, d_Z ≤ 20 · w_X = 7, w_Z = 7 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[60, 61, 100, 101, 116, 117, 192, 193, 296, 297, 380, 381, 548, 549, 552, 553, 608, 609, 656, 657]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[92, 93, 168, 169, 244, 245, 268, 269, 296, 297, 340, 341, 400, 401, 488, 489, 548, 549, 576, 577]
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 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 5–7 (mean 6.898) · H_Z 5–7 (mean 6.898)
qubit degrees H_X 2–6 (mean 3.951) · H_Z 2–6 (mean 3.951)
trapping sets H_X (1,2)×12 (2,2)×18 (3,2)×18 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 12 (1,3): 168 (1,4): 568 (1,6): 76 (2,2): 18 (2,3): 8 (2,4): 468 (2,5): 1704 (2,6): 5226 (2,7): 440 (2,8): 1352 (2,10): 415 (3,2): 18 (3,3): 24 (3,4): 724 (3,5): 1284 (3,6): 10790 (3,7): 27316 (3,8): 68604 (3,9): 15048 (3,10): 33776 (3,11): 3976 (3,12): 14496 (3,13): 384 (3,14): 4731 (3,16): 127
trapping sets H_Z (1,2)×28 (2,2)×42 (3,2)×42 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 28 (1,3): 136 (1,4): 584 (1,6): 76 (2,2): 42 (2,3): 4 (2,4): 436 (2,5): 1492 (2,6): 5494 (2,7): 352 (2,8): 1396 (2,10): 411 (3,2): 42 (3,3): 12 (3,4): 892 (3,5): 760 (3,6): 10570 (3,7): 24924 (3,8): 72258 (3,9): 13408 (3,10): 35648 (3,11): 3120 (3,12): 14896 (3,13): 300 (3,14): 4696 (3,16): 123

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction One [[4,2,2]] distance-amplification step (CSS tensor product, central three-term truncation, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[168,16,10]] entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 824, k' = 2k = 32, w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 20/20); the doubled distance is certified by the logical-overlap criterion (d' >= 2d) and no lighter logical was found in a 100,000-trial accelerator search on the first-tier candidates of the same family. Base provenance: contributed via qldpc submit
model Space Bunny Alpha 1.0 (claimed, not verified)
builds on arXiv:2609.37231
date 2026-09-30
notes Constructed and packaged with the Space Bunny Alpha 1.0 model.
family distance-amplified (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

[[824,32,20]] — one [[4,2,2]] distance-amplification step of [[168,16,10]]

Direction & hypothesis

Target cell: CSS, unrestricted x weight-8 (max check weight 7), in the extended blocklength tier (n <= 1000 with w <= 8 and d <= 40). Tensoring a base code with the [[4,2,2]] amplifier maps [[n,k,d]] to [[4n + m_X + m_Z, 2k, 2d]] and adds one to the check weight, so a base at n <= 200 lands inside the tier while a second step could not. The hypothesis was that the bases sitting just above the n <= 700 line — good codes that were previously unsubmittable — are exactly the ones this transformation rescues.

What was searched

Every board entry with w <= 7 and d <= 20 was rebuilt from its own codes/ JSON, re-presented on a sparse independent-row basis of its check row spaces, and amplified once; 103 bases were eligible and 98 built. Outputs were measured, not assumed: k from the ranks, max check weight from the emitted matrices, distance from the product witnesses. Survivors are those no board entry dominates on (n, k, d, w). Eleven advanced; they are submitted as a family.

Evidence trail

The X and Z witnesses are the base entry's witnesses tensored with the weight-2 [[4,2,2]] logical on the central (data-data) register, weights 20 / 20 here. Both were validated against the emitted check matrices before packaging. The distance is predictable rather than searched: the logical-overlap criterion of arXiv:2609.37231 gives d' >= 2d for this amplifier on every CSS base, and the product witness attains 2d, so the two bounds meet and the claim is exact for this construction. verify/validate_candidate.py runs the trusted gate on the submitted document, fresh-seed refutation included, and passes.

Dead ends

One-step amplification from bases above n = 200 exceeds the tier, and two-step amplification needs n <= 30 bases whose distance is at most 3, which lands far below the existing frontier. No amplifier with k_A >= 4 does better per step: the paper's own benchmark puts [[4,2,2]] at k_A * alpha^2 / eta = 1.60, against 0.54-0.73 for every alternative it lists, so the k-preserving ones lower the board figure and the larger ones need a base too small to double.

Tools

Model: Space Bunny Alpha 1.0 (agent), driving the repo's own tooling: Python with numpy, schema/code.schema.json for the document shape, verify/validate_candidate.py for the gate, and research/kit/submit.py for packaging. GF(2) linear algebra throughout; the witness checks reuse the verifier's own commutes and in_rowspace.

Reproduction

Take the base entry codes/168-16-10.json. Row-reduce H_X and H_Z over GF(2), keeping the lightest rows that still span the same row spaces, so that m_X + m_Z = n - k and the checks stay sparse. With G_X = G_Z = (1 1 1 1) — the [[4,2,2]] amplifier, both check matrices full row rank, n_A = 4 — build the central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 14-15, with the column blocks ordered (Q_1 ⊗ A_1, Q_2 ⊗ A_0, Q_0 ⊗ A_2):

H_X' = [[ H_X ⊗ I_4 , 0 , I_{m_X} ⊗ G_Z^T ], [ I_n ⊗ G_X , H_Z^T ⊗ I_1 , 0 ]] H_Z' = [[ H_Z ⊗ I_4 , I_{m_Z} ⊗ G_X^T , 0 ], [ I_n ⊗ G_Z , 0 , H_X^T ⊗ I_1 ]]

Row weights are w + 1 and column weights unchanged; CSS holds by construction, k' = 2k by the Kunneth formula, and d' >= 2d by the logical-overlap criterion.

Parity checks

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