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[[708,24,24]] d ≤
n
708
k
24
d
24
kd²/n
19.525
w
7
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 24, d_Z ≤ 24 · 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 24 · witness weight 24 (claimed upper_bound)
witness operator (support, 24 qubits)
[216, 217, 224, 225, 240, 241, 256, 257, 268, 269, 284, 285, 504, 505, 508, 509, 520, 521, 524, 525, 532, 533, 548, 549]
d_Z 24 · witness weight 24 (claimed upper_bound)
witness operator (support, 24 qubits)
[0, 1, 40, 41, 68, 69, 288, 289, 304, 305, 312, 313, 324, 325, 328, 329, 332, 333, 336, 337, 340, 341, 552, 553]
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 6.912) · H_Z 5–7 (mean 6.912)
qubit degrees H_X 2–6 (mean 3.983) · H_Z 2–6 (mean 3.983)
trapping sets H_X (1,2)×16 (2,2)×24 (3,2)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 16 (1,3): 112 (1,4): 514 (1,6): 66 (2,2): 24 (2,3): 8 (2,4): 316 (2,5): 1216 (2,6): 4884 (2,7): 296 (2,8): 1248 (2,10): 364 (3,2): 24 (3,3): 24 (3,4): 608 (3,5): 672 (3,6): 8120 (3,7): 20392 (3,8): 64792 (3,9): 11064 (3,10): 32256 (3,11): 2744 (3,12): 13456 (3,13): 264 (3,14): 4163 (3,16): 112
trapping sets H_Z (1,2)×16 (2,2)×24 (3,2)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 16 (1,3): 112 (1,4): 514 (1,6): 66 (2,2): 24 (2,3): 4 (2,4): 328 (2,5): 1204 (2,6): 4888 (2,7): 296 (2,8): 1248 (2,10): 364 (3,2): 24 (3,3): 12 (3,4): 604 (3,5): 676 (3,6): 8316 (3,7): 20012 (3,8): 65104 (3,9): 10884 (3,10): 32316 (3,11): 2752 (3,12): 13452 (3,13): 264 (3,14): 4163 (3,16): 112

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 [[144,12,12]] bivariate bicycle code entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 708, k' = 2k = 24, 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 24/24); 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: Bivariate bicycle code, orders (12, 6), A=x3 + y2 + y, B=x2 + x + y3 (periodic boundary conditions).
model Space Bunny Alpha 1.0 (claimed, not verified)
builds on arXiv:2609.37231, arXiv:2308.07915
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

[[708,24,24]] — one [[4,2,2]] distance-amplification step of [[144,12,12]]

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