← back to the board
[[378,4,48]] d ≤
n
378
k
4
d
48
kd²/n
24.381
w
15
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 48, d_Z ≤ 48 · w_X = 15, w_Z = 15 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 48 · witness weight 48 (claimed upper_bound)
witness found by @vprusso · gate_changed.py RIS-fast (CI refuter) · found at 8×106 trials · survived 5×107 trials · 2026-09-24
witness operator (support, 48 qubits)
[5, 9, 17, 19, 29, 45, 59, 67, 72, 74, 80, 81, 84, 86, 89, 109, 111, 141, 142, 158, 163, 183, 191, 208, 211, 218, 224, 236, 237, 244, 252, 263, 269, 277, 292, 294, 303, 306, 308, 314, 332, 336, 357, 361, 365, 373, 374, 376]
d_Z 48 · witness weight 48 (claimed upper_bound)
witness found by @vprusso · norm-lift quotient bound, m' = 63, quotient weight 16 · found at 1 trials · survived 5×107 trials · 2026-09-24
witness operator (support, 48 qubits)
[6, 11, 15, 21, 40, 49, 69, 74, 78, 84, 103, 112, 132, 137, 141, 147, 166, 175, 193, 200, 201, 202, 213, 218, 221, 223, 226, 228, 256, 263, 264, 265, 276, 281, 284, 286, 289, 291, 319, 326, 327, 328, 339, 344, 347, 349, 352, 354]
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 15 · H_Z 15
qubit degrees H_X 6–9 (mean 7.5) · H_Z 6–9 (mean 7.5)
trapping sets H_X (1,6)×189 (2,10)×2835 (3,12)×8127 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,6): 189 (1,9): 189 (2,10): 2835 (2,11): 945 (2,12): 189 (2,13): 8316 (2,14): 378 (2,16): 5481 (3,12): 8127 (3,13): 3969 (3,14): 48951 (3,15): 64071 (3,16): 27216 (3,17): 329805 (3,18): 120015 (3,19): 32697 (3,20): 464562 (3,21): 52164 (3,22): 21546 (3,23): 202230 (3,25): 8694
trapping sets H_Z (1,6)×189 (2,10)×2835 (3,12)×8127 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,6): 189 (1,9): 189 (2,10): 2835 (2,11): 945 (2,12): 189 (2,13): 8316 (2,14): 378 (2,16): 5481 (3,12): 8127 (3,13): 3969 (3,14): 48951 (3,15): 64071 (3,16): 27216 (3,17): 329805 (3,18): 120015 (3,19): 32697 (3,20): 464562 (3,21): 52164 (3,22): 21546 (3,23): 202230 (3,25): 8694

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Cyclic generalized-bicycle code on the ring x189 - 1 with a(x) = x35 + x48 + x62 + x94 + x99 + x113 + x127 + x130 + x180, b(x) = x19 + x34 + x76 + x136 + x146 + x173; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].
model Claude Claude Opus 5 (claimed, not verified)
date 2026-09-24
notes Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed.
family generalized bicycle (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

[[378,4,48]] weight-15 cyclic generalized-bicycle

Hypothesis

Cyclic generalized-bicycle codes at check weight 15 cover a wide blocklength range, and the board's coverage of that range is uneven: there are stretches of n where no entry sits near the (k, d) the family can reach. A broad randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work, finds the gaps.

Construction

ring x^189 - 1 a(x) = x^35 + x^48 + x^62 + x^94 + x^99 + x^113 + x^127 + x^130 + x^180 b(x) = x^19 + x^34 + x^76 + x^136 + x^146 + x^173 H_X = [circ(a) | circ(b)] H_Z = [circ(b)^T | circ(a)^T]

n = 2m, and k = 2 deg gcd(a, b, x^m - 1), computed by Euclid before any matrix work so that most draws are discarded for free.

What was swept

One loop draws a ring size and a weight split, samples the two sparse polynomials, computes k by Euclid, and runs a cheap 60k-trial distance screen. A draw survives only if the resulting (n, k, d, w) is undominated on the live board snapshot. Surviving draws go through an escalating ladder of 400k, 2M and 8M random information-set trials, with the board comparison repeated at each rung so a candidate that collapses is dropped as soon as it stops being interesting.

The single-block check

General RIS over all 2m columns is close to blind to a logical supported entirely on one block. Such a vector u satisfies a(x) u(x) = 0 mod x^m - 1, which puts u in the ideal generated by h = (x^m - 1) / gcd(a, x^m - 1), so it can be searched directly in a space of dimension deg h rather than 2m. This matters: a previous submission of mine survived 150M general RIS trials at weight 74 and was then refuted by a weight-64 logical sitting entirely in one block, which the ideal search finds in seconds. Every candidate here is checked that way before the distance is believed, and any candidate whose single-block bound comes in below the ladder is dropped rather than submitted.

Distance ladder

Witness search runs on each side separately, so a run that happens to find one side cannot leave the other without a witness. Both witnesses are re-checked directly against H: in the kernel of the opposite matrix, and outside the row space of its own.

What it advances

Score kd^2/n = 24.381 at check weight 15. Undominated in its cell against the board at submission time.

Boundary

The distance is an upper bound from witness search, not a proof. Literature novelty is unverified: cyclic GB codes are a classical family and these parameters may appear in the 2BGA literature.

Correction after the gate

First filed as [[378,4,52]]. The verifier's RIS-fast refutation pass (8,000,000 trials, seed 1587648752) found a weight-48 logical, below the 8M-trial ladder of the sweep.

Three deeper searches followed. The single-block constituent bound, exhaustive over each block kernel, is 63 on the X side and 63 on the Z side. The norm-lift quotient bound (reduce exponents modulo a divisor m' of m = 189, find a light kernel word of the quotient code, and multiply it by the norm element 1 + x^m' + ... + x^(m - m')) gives weight 48 on the X side (m' = 63) and 48 on the Z side (m' = 63). A GPU random-information-set search (verify/ris_gpu.py, recover mode, pair depth 8, 50,000,000 trials per side per seed, seeds 201) reached weight 50 on the X side and 52 on the Z side.

The lightest CPU-validated logical per side is a weight-48 X logical from the CI gate and a weight-48 Z logical from the norm-lift quotient bound, so the entry is filed at [[378,4,48]] (X 48, Z 48), kd^2/n 28.614 -> 24.381. Each witness is carried in the code file with the budget it was found at and, where the GPU pass tested it without finding anything lighter, the budget it survived. The distance remains an upper bound.

Parity checks

X-checks 189 (max weight 15) · Z-checks 189 (max weight 15)
H_X (189 checks, sparse supports)
[35, 48, 62, 94, 99, 113, 127, 130, 180, 208, 223, 265, 325, 335, 362] [36, 49, 63, 95, 100, 114, 128, 131, 181, 209, 224, 266, 326, 336, 363] [37, 50, 64, 96, 101, 115, 129, 132, 182, 210, 225, 267, 327, 337, 364] [38, 51, 65, 97, 102, 116, 130, 133, 183, 211, 226, 268, 328, 338, 365] [39, 52, 66, 98, 103, 117, 131, 134, 184, 212, 227, 269, 329, 339, 366] [40, 53, 67, 99, 104, 118, 132, 135, 185, 213, 228, 270, 330, 340, 367] [41, 54, 68, 100, 105, 119, 133, 136, 186, 214, 229, 271, 331, 341, 368] [42, 55, 69, 101, 106, 120, 134, 137, 187, 215, 230, 272, 332, 342, 369] [43, 56, 70, 102, 107, 121, 135, 138, 188, 216, 231, 273, 333, 343, 370] [0, 44, 57, 71, 103, 108, 122, 136, 139, 217, 232, 274, 334, 344, 371] [1, 45, 58, 72, 104, 109, 123, 137, 140, 218, 233, 275, 335, 345, 372] [2, 46, 59, 73, 105, 110, 124, 138, 141, 219, 234, 276, 336, 346, 373] [3, 47, 60, 74, 106, 111, 125, 139, 142, 220, 235, 277, 337, 347, 374] [4, 48, 61, 75, 107, 112, 126, 140, 143, 221, 236, 278, 338, 348, 375] [5, 49, 62, 76, 108, 113, 127, 141, 144, 222, 237, 279, 339, 349, 376] [6, 50, 63, 77, 109, 114, 128, 142, 145, 223, 238, 280, 340, 350, 377] [7, 51, 64, 78, 110, 115, 129, 143, 146, 189, 224, 239, 281, 341, 351] [8, 52, 65, 79, 111, 116, 130, 144, 147, 190, 225, 240, 282, 342, 352] [9, 53, 66, 80, 112, 117, 131, 145, 148, 191, 226, 241, 283, 343, 353] [10, 54, 67, 81, 113, 118, 132, 146, 149, 192, 227, 242, 284, 344, 354] [11, 55, 68, 82, 114, 119, 133, 147, 150, 193, 228, 243, 285, 345, 355] [12, 56, 69, 83, 115, 120, 134, 148, 151, 194, 229, 244, 286, 346, 356] [13, 57, 70, 84, 116, 121, 135, 149, 152, 195, 230, 245, 287, 347, 357] [14, 58, 71, 85, 117, 122, 136, 150, 153, 196, 231, 246, 288, 348, 358] [15, 59, 72, 86, 118, 123, 137, 151, 154, 197, 232, 247, 289, 349, 359] [16, 60, 73, 87, 119, 124, 138, 152, 155, 198, 233, 248, 290, 350, 360] [17, 61, 74, 88, 120, 125, 139, 153, 156, 199, 234, 249, 291, 351, 361] [18, 62, 75, 89, 121, 126, 140, 154, 157, 200, 235, 250, 292, 352, 362] [19, 63, 76, 90, 122, 127, 141, 155, 158, 201, 236, 251, 293, 353, 363] [20, 64, 77, 91, 123, 128, 142, 156, 159, 202, 237, 252, 294, 354, 364] [21, 65, 78, 92, 124, 129, 143, 157, 160, 203, 238, 253, 295, 355, 365] [22, 66, 79, 93, 125, 130, 144, 158, 161, 204, 239, 254, 296, 356, 366] [23, 67, 80, 94, 126, 131, 145, 159, 162, 205, 240, 255, 297, 357, 367] [24, 68, 81, 95, 127, 132, 146, 160, 163, 206, 241, 256, 298, 358, 368] [25, 69, 82, 96, 128, 133, 147, 161, 164, 207, 242, 257, 299, 359, 369] [26, 70, 83, 97, 129, 134, 148, 162, 165, 208, 243, 258, 300, 360, 370] [27, 71, 84, 98, 130, 135, 149, 163, 166, 209, 244, 259, 301, 361, 371] [28, 72, 85, 99, 131, 136, 150, 164, 167, 210, 245, 260, 302, 362, 372] [29, 73, 86, 100, 132, 137, 151, 165, 168, 211, 246, 261, 303, 363, 373] [30, 74, 87, 101, 133, 138, 152, 166, 169, 212, 247, 262, 304, 364, 374] [31, 75, 88, 102, 134, 139, 153, 167, 170, 213, 248, 263, 305, 365, 375] [32, 76, 89, 103, 135, 140, 154, 168, 171, 214, 249, 264, 306, 366, 376] [33, 77, 90, 104, 136, 141, 155, 169, 172, 215, 250, 265, 307, 367, 377] [34, 78, 91, 105, 137, 142, 156, 170, 173, 189, 216, 251, 266, 308, 368] [35, 79, 92, 106, 138, 143, 157, 171, 174, 190, 217, 252, 267, 309, 369] [36, 80, 93, 107, 139, 144, 158, 172, 175, 191, 218, 253, 268, 310, 370] [37, 81, 94, 108, 140, 145, 159, 173, 176, 192, 219, 254, 269, 311, 371] [38, 82, 95, 109, 141, 146, 160, 174, 177, 193, 220, 255, 270, 312, 372] [39, 83, 96, 110, 142, 147, 161, 175, 178, 194, 221, 256, 271, 313, 373] [40, 84, 97, 111, 143, 148, 162, 176, 179, 195, 222, 257, 272, 314, 374] [41, 85, 98, 112, 144, 149, 163, 177, 180, 196, 223, 258, 273, 315, 375] [42, 86, 99, 113, 145, 150, 164, 178, 181, 197, 224, 259, 274, 316, 376] [43, 87, 100, 114, 146, 151, 165, 179, 182, 198, 225, 260, 275, 317, 377] [44, 88, 101, 115, 147, 152, 166, 180, 183, 189, 199, 226, 261, 276, 318] [45, 89, 102, 116, 148, 153, 167, 181, 184, 190, 200, 227, 262, 277, 319] [46, 90, 103, 117, 149, 154, 168, 182, 185, 191, 201, 228, 263, 278, 320] [47, 91, 104, 118, 150, 155, 169, 183, 186, 192, 202, 229, 264, 279, 321] [48, 92, 105, 119, 151, 156, 170, 184, 187, 193, 203, 230, 265, 280, 322] [49, 93, 106, 120, 152, 157, 171, 185, 188, 194, 204, 231, 266, 281, 323] [0, 50, 94, 107, 121, 153, 158, 172, 186, 195, 205, 232, 267, 282, 324] [1, 51, 95, 108, 122, 154, 159, 173, 187, 196, 206, 233, 268, 283, 325] [2, 52, 96, 109, 123, 155, 160, 174, 188, 197, 207, 234, 269, 284, 326] [0, 3, 53, 97, 110, 124, 156, 161, 175, 198, 208, 235, 270, 285, 327] [1, 4, 54, 98, 111, 125, 157, 162, 176, 199, 209, 236, 271, 286, 328] [2, 5, 55, 99, 112, 126, 158, 163, 177, 200, 210, 237, 272, 287, 329] [3, 6, 56, 100, 113, 127, 159, 164, 178, 201, 211, 238, 273, 288, 330] [4, 7, 57, 101, 114, 128, 160, 165, 179, 202, 212, 239, 274, 289, 331] [5, 8, 58, 102, 115, 129, 161, 166, 180, 203, 213, 240, 275, 290, 332] [6, 9, 59, 103, 116, 130, 162, 167, 181, 204, 214, 241, 276, 291, 333] [7, 10, 60, 104, 117, 131, 163, 168, 182, 205, 215, 242, 277, 292, 334] [8, 11, 61, 105, 118, 132, 164, 169, 183, 206, 216, 243, 278, 293, 335] [9, 12, 62, 106, 119, 133, 165, 170, 184, 207, 217, 244, 279, 294, 336] [10, 13, 63, 107, 120, 134, 166, 171, 185, 208, 218, 245, 280, 295, 337] [11, 14, 64, 108, 121, 135, 167, 172, 186, 209, 219, 246, 281, 296, 338] [12, 15, 65, 109, 122, 136, 168, 173, 187, 210, 220, 247, 282, 297, 339] [13, 16, 66, 110, 123, 137, 169, 174, 188, 211, 221, 248, 283, 298, 340] [0, 14, 17, 67, 111, 124, 138, 170, 175, 212, 222, 249, 284, 299, 341] [1, 15, 18, 68, 112, 125, 139, 171, 176, 213, 223, 250, 285, 300, 342] [2, 16, 19, 69, 113, 126, 140, 172, 177, 214, 224, 251, 286, 301, 343] [3, 17, 20, 70, 114, 127, 141, 173, 178, 215, 225, 252, 287, 302, 344] [4, 18, 21, 71, 115, 128, 142, 174, 179, 216, 226, 253, 288, 303, 345] [5, 19, 22, 72, 116, 129, 143, 175, 180, 217, 227, 254, 289, 304, 346] [6, 20, 23, 73, 117, 130, 144, 176, 181, 218, 228, 255, 290, 305, 347] [7, 21, 24, 74, 118, 131, 145, 177, 182, 219, 229, 256, 291, 306, 348] [8, 22, 25, 75, 119, 132, 146, 178, 183, 220, 230, 257, 292, 307, 349] [9, 23, 26, 76, 120, 133, 147, 179, 184, 221, 231, 258, 293, 308, 350] [10, 24, 27, 77, 121, 134, 148, 180, 185, 222, 232, 259, 294, 309, 351] [11, 25, 28, 78, 122, 135, 149, 181, 186, 223, 233, 260, 295, 310, 352] [12, 26, 29, 79, 123, 136, 150, 182, 187, 224, 234, 261, 296, 311, 353] [13, 27, 30, 80, 124, 137, 151, 183, 188, 225, 235, 262, 297, 312, 354] [0, 14, 28, 31, 81, 125, 138, 152, 184, 226, 236, 263, 298, 313, 355] [1, 15, 29, 32, 82, 126, 139, 153, 185, 227, 237, 264, 299, 314, 356] [2, 16, 30, 33, 83, 127, 140, 154, 186, 228, 238, 265, 300, 315, 357] [3, 17, 31, 34, 84, 128, 141, 155, 187, 229, 239, 266, 301, 316, 358] [4, 18, 32, 35, 85, 129, 142, 156, 188, 230, 240, 267, 302, 317, 359] [0, 5, 19, 33, 36, 86, 130, 143, 157, 231, 241, 268, 303, 318, 360] [1, 6, 20, 34, 37, 87, 131, 144, 158, 232, 242, 269, 304, 319, 361] [2, 7, 21, 35, 38, 88, 132, 145, 159, 233, 243, 270, 305, 320, 362] [3, 8, 22, 36, 39, 89, 133, 146, 160, 234, 244, 271, 306, 321, 363] [4, 9, 23, 37, 40, 90, 134, 147, 161, 235, 245, 272, 307, 322, 364] [5, 10, 24, 38, 41, 91, 135, 148, 162, 236, 246, 273, 308, 323, 365] [6, 11, 25, 39, 42, 92, 136, 149, 163, 237, 247, 274, 309, 324, 366] [7, 12, 26, 40, 43, 93, 137, 150, 164, 238, 248, 275, 310, 325, 367] [8, 13, 27, 41, 44, 94, 138, 151, 165, 239, 249, 276, 311, 326, 368] [9, 14, 28, 42, 45, 95, 139, 152, 166, 240, 250, 277, 312, 327, 369] [10, 15, 29, 43, 46, 96, 140, 153, 167, 241, 251, 278, 313, 328, 370] [11, 16, 30, 44, 47, 97, 141, 154, 168, 242, 252, 279, 314, 329, 371] [12, 17, 31, 45, 48, 98, 142, 155, 169, 243, 253, 280, 315, 330, 372] [13, 18, 32, 46, 49, 99, 143, 156, 170, 244, 254, 281, 316, 331, 373] [14, 19, 33, 47, 50, 100, 144, 157, 171, 245, 255, 282, 317, 332, 374] [15, 20, 34, 48, 51, 101, 145, 158, 172, 246, 256, 283, 318, 333, 375] [16, 21, 35, 49, 52, 102, 146, 159, 173, 247, 257, 284, 319, 334, 376] [17, 22, 36, 50, 53, 103, 147, 160, 174, 248, 258, 285, 320, 335, 377] [18, 23, 37, 51, 54, 104, 148, 161, 175, 189, 249, 259, 286, 321, 336] [19, 24, 38, 52, 55, 105, 149, 162, 176, 190, 250, 260, 287, 322, 337] [20, 25, 39, 53, 56, 106, 150, 163, 177, 191, 251, 261, 288, 323, 338] [21, 26, 40, 54, 57, 107, 151, 164, 178, 192, 252, 262, 289, 324, 339] [22, 27, 41, 55, 58, 108, 152, 165, 179, 193, 253, 263, 290, 325, 340] [23, 28, 42, 56, 59, 109, 153, 166, 180, 194, 254, 264, 291, 326, 341] [24, 29, 43, 57, 60, 110, 154, 167, 181, 195, 255, 265, 292, 327, 342] [25, 30, 44, 58, 61, 111, 155, 168, 182, 196, 256, 266, 293, 328, 343] [26, 31, 45, 59, 62, 112, 156, 169, 183, 197, 257, 267, 294, 329, 344] [27, 32, 46, 60, 63, 113, 157, 170, 184, 198, 258, 268, 295, 330, 345] [28, 33, 47, 61, 64, 114, 158, 171, 185, 199, 259, 269, 296, 331, 346] [29, 34, 48, 62, 65, 115, 159, 172, 186, 200, 260, 270, 297, 332, 347] [30, 35, 49, 63, 66, 116, 160, 173, 187, 201, 261, 271, 298, 333, 348] [31, 36, 50, 64, 67, 117, 161, 174, 188, 202, 262, 272, 299, 334, 349] [0, 32, 37, 51, 65, 68, 118, 162, 175, 203, 263, 273, 300, 335, 350] [1, 33, 38, 52, 66, 69, 119, 163, 176, 204, 264, 274, 301, 336, 351] [2, 34, 39, 53, 67, 70, 120, 164, 177, 205, 265, 275, 302, 337, 352] [3, 35, 40, 54, 68, 71, 121, 165, 178, 206, 266, 276, 303, 338, 353] [4, 36, 41, 55, 69, 72, 122, 166, 179, 207, 267, 277, 304, 339, 354] [5, 37, 42, 56, 70, 73, 123, 167, 180, 208, 268, 278, 305, 340, 355] [6, 38, 43, 57, 71, 74, 124, 168, 181, 209, 269, 279, 306, 341, 356] [7, 39, 44, 58, 72, 75, 125, 169, 182, 210, 270, 280, 307, 342, 357] [8, 40, 45, 59, 73, 76, 126, 170, 183, 211, 271, 281, 308, 343, 358] [9, 41, 46, 60, 74, 77, 127, 171, 184, 212, 272, 282, 309, 344, 359] [10, 42, 47, 61, 75, 78, 128, 172, 185, 213, 273, 283, 310, 345, 360] [11, 43, 48, 62, 76, 79, 129, 173, 186, 214, 274, 284, 311, 346, 361] [12, 44, 49, 63, 77, 80, 130, 174, 187, 215, 275, 285, 312, 347, 362] [13, 45, 50, 64, 78, 81, 131, 175, 188, 216, 276, 286, 313, 348, 363] [0, 14, 46, 51, 65, 79, 82, 132, 176, 217, 277, 287, 314, 349, 364] [1, 15, 47, 52, 66, 80, 83, 133, 177, 218, 278, 288, 315, 350, 365] [2, 16, 48, 53, 67, 81, 84, 134, 178, 219, 279, 289, 316, 351, 366] [3, 17, 49, 54, 68, 82, 85, 135, 179, 220, 280, 290, 317, 352, 367] [4, 18, 50, 55, 69, 83, 86, 136, 180, 221, 281, 291, 318, 353, 368] [5, 19, 51, 56, 70, 84, 87, 137, 181, 222, 282, 292, 319, 354, 369] [6, 20, 52, 57, 71, 85, 88, 138, 182, 223, 283, 293, 320, 355, 370] [7, 21, 53, 58, 72, 86, 89, 139, 183, 224, 284, 294, 321, 356, 371] [8, 22, 54, 59, 73, 87, 90, 140, 184, 225, 285, 295, 322, 357, 372] [9, 23, 55, 60, 74, 88, 91, 141, 185, 226, 286, 296, 323, 358, 373] [10, 24, 56, 61, 75, 89, 92, 142, 186, 227, 287, 297, 324, 359, 374] [11, 25, 57, 62, 76, 90, 93, 143, 187, 228, 288, 298, 325, 360, 375] [12, 26, 58, 63, 77, 91, 94, 144, 188, 229, 289, 299, 326, 361, 376] [0, 13, 27, 59, 64, 78, 92, 95, 145, 230, 290, 300, 327, 362, 377] [1, 14, 28, 60, 65, 79, 93, 96, 146, 189, 231, 291, 301, 328, 363] [2, 15, 29, 61, 66, 80, 94, 97, 147, 190, 232, 292, 302, 329, 364] [3, 16, 30, 62, 67, 81, 95, 98, 148, 191, 233, 293, 303, 330, 365] [4, 17, 31, 63, 68, 82, 96, 99, 149, 192, 234, 294, 304, 331, 366] [5, 18, 32, 64, 69, 83, 97, 100, 150, 193, 235, 295, 305, 332, 367] [6, 19, 33, 65, 70, 84, 98, 101, 151, 194, 236, 296, 306, 333, 368] [7, 20, 34, 66, 71, 85, 99, 102, 152, 195, 237, 297, 307, 334, 369] [8, 21, 35, 67, 72, 86, 100, 103, 153, 196, 238, 298, 308, 335, 370] [9, 22, 36, 68, 73, 87, 101, 104, 154, 197, 239, 299, 309, 336, 371] [10, 23, 37, 69, 74, 88, 102, 105, 155, 198, 240, 300, 310, 337, 372] [11, 24, 38, 70, 75, 89, 103, 106, 156, 199, 241, 301, 311, 338, 373] [12, 25, 39, 71, 76, 90, 104, 107, 157, 200, 242, 302, 312, 339, 374] [13, 26, 40, 72, 77, 91, 105, 108, 158, 201, 243, 303, 313, 340, 375] [14, 27, 41, 73, 78, 92, 106, 109, 159, 202, 244, 304, 314, 341, 376] [15, 28, 42, 74, 79, 93, 107, 110, 160, 203, 245, 305, 315, 342, 377] [16, 29, 43, 75, 80, 94, 108, 111, 161, 189, 204, 246, 306, 316, 343] [17, 30, 44, 76, 81, 95, 109, 112, 162, 190, 205, 247, 307, 317, 344] [18, 31, 45, 77, 82, 96, 110, 113, 163, 191, 206, 248, 308, 318, 345] [19, 32, 46, 78, 83, 97, 111, 114, 164, 192, 207, 249, 309, 319, 346] [20, 33, 47, 79, 84, 98, 112, 115, 165, 193, 208, 250, 310, 320, 347] [21, 34, 48, 80, 85, 99, 113, 116, 166, 194, 209, 251, 311, 321, 348] [22, 35, 49, 81, 86, 100, 114, 117, 167, 195, 210, 252, 312, 322, 349] [23, 36, 50, 82, 87, 101, 115, 118, 168, 196, 211, 253, 313, 323, 350] [24, 37, 51, 83, 88, 102, 116, 119, 169, 197, 212, 254, 314, 324, 351] [25, 38, 52, 84, 89, 103, 117, 120, 170, 198, 213, 255, 315, 325, 352] [26, 39, 53, 85, 90, 104, 118, 121, 171, 199, 214, 256, 316, 326, 353] [27, 40, 54, 86, 91, 105, 119, 122, 172, 200, 215, 257, 317, 327, 354] [28, 41, 55, 87, 92, 106, 120, 123, 173, 201, 216, 258, 318, 328, 355] [29, 42, 56, 88, 93, 107, 121, 124, 174, 202, 217, 259, 319, 329, 356] [30, 43, 57, 89, 94, 108, 122, 125, 175, 203, 218, 260, 320, 330, 357] [31, 44, 58, 90, 95, 109, 123, 126, 176, 204, 219, 261, 321, 331, 358] [32, 45, 59, 91, 96, 110, 124, 127, 177, 205, 220, 262, 322, 332, 359] [33, 46, 60, 92, 97, 111, 125, 128, 178, 206, 221, 263, 323, 333, 360] [34, 47, 61, 93, 98, 112, 126, 129, 179, 207, 222, 264, 324, 334, 361]
H_Z (189 checks, sparse supports)
[16, 43, 53, 113, 155, 170, 198, 248, 251, 265, 279, 284, 316, 330, 343] [17, 44, 54, 114, 156, 171, 199, 249, 252, 266, 280, 285, 317, 331, 344] [18, 45, 55, 115, 157, 172, 200, 250, 253, 267, 281, 286, 318, 332, 345] [19, 46, 56, 116, 158, 173, 201, 251, 254, 268, 282, 287, 319, 333, 346] [20, 47, 57, 117, 159, 174, 202, 252, 255, 269, 283, 288, 320, 334, 347] [21, 48, 58, 118, 160, 175, 203, 253, 256, 270, 284, 289, 321, 335, 348] [22, 49, 59, 119, 161, 176, 204, 254, 257, 271, 285, 290, 322, 336, 349] [23, 50, 60, 120, 162, 177, 205, 255, 258, 272, 286, 291, 323, 337, 350] [24, 51, 61, 121, 163, 178, 206, 256, 259, 273, 287, 292, 324, 338, 351] [25, 52, 62, 122, 164, 179, 207, 257, 260, 274, 288, 293, 325, 339, 352] [26, 53, 63, 123, 165, 180, 208, 258, 261, 275, 289, 294, 326, 340, 353] [27, 54, 64, 124, 166, 181, 209, 259, 262, 276, 290, 295, 327, 341, 354] [28, 55, 65, 125, 167, 182, 210, 260, 263, 277, 291, 296, 328, 342, 355] [29, 56, 66, 126, 168, 183, 211, 261, 264, 278, 292, 297, 329, 343, 356] [30, 57, 67, 127, 169, 184, 212, 262, 265, 279, 293, 298, 330, 344, 357] [31, 58, 68, 128, 170, 185, 213, 263, 266, 280, 294, 299, 331, 345, 358] [32, 59, 69, 129, 171, 186, 214, 264, 267, 281, 295, 300, 332, 346, 359] [33, 60, 70, 130, 172, 187, 215, 265, 268, 282, 296, 301, 333, 347, 360] [34, 61, 71, 131, 173, 188, 216, 266, 269, 283, 297, 302, 334, 348, 361] [0, 35, 62, 72, 132, 174, 217, 267, 270, 284, 298, 303, 335, 349, 362] [1, 36, 63, 73, 133, 175, 218, 268, 271, 285, 299, 304, 336, 350, 363] [2, 37, 64, 74, 134, 176, 219, 269, 272, 286, 300, 305, 337, 351, 364] [3, 38, 65, 75, 135, 177, 220, 270, 273, 287, 301, 306, 338, 352, 365] [4, 39, 66, 76, 136, 178, 221, 271, 274, 288, 302, 307, 339, 353, 366] [5, 40, 67, 77, 137, 179, 222, 272, 275, 289, 303, 308, 340, 354, 367] [6, 41, 68, 78, 138, 180, 223, 273, 276, 290, 304, 309, 341, 355, 368] [7, 42, 69, 79, 139, 181, 224, 274, 277, 291, 305, 310, 342, 356, 369] [8, 43, 70, 80, 140, 182, 225, 275, 278, 292, 306, 311, 343, 357, 370] [9, 44, 71, 81, 141, 183, 226, 276, 279, 293, 307, 312, 344, 358, 371] [10, 45, 72, 82, 142, 184, 227, 277, 280, 294, 308, 313, 345, 359, 372] [11, 46, 73, 83, 143, 185, 228, 278, 281, 295, 309, 314, 346, 360, 373] [12, 47, 74, 84, 144, 186, 229, 279, 282, 296, 310, 315, 347, 361, 374] [13, 48, 75, 85, 145, 187, 230, 280, 283, 297, 311, 316, 348, 362, 375] [14, 49, 76, 86, 146, 188, 231, 281, 284, 298, 312, 317, 349, 363, 376] [0, 15, 50, 77, 87, 147, 232, 282, 285, 299, 313, 318, 350, 364, 377] [1, 16, 51, 78, 88, 148, 189, 233, 283, 286, 300, 314, 319, 351, 365] [2, 17, 52, 79, 89, 149, 190, 234, 284, 287, 301, 315, 320, 352, 366] [3, 18, 53, 80, 90, 150, 191, 235, 285, 288, 302, 316, 321, 353, 367] [4, 19, 54, 81, 91, 151, 192, 236, 286, 289, 303, 317, 322, 354, 368] [5, 20, 55, 82, 92, 152, 193, 237, 287, 290, 304, 318, 323, 355, 369] [6, 21, 56, 83, 93, 153, 194, 238, 288, 291, 305, 319, 324, 356, 370] [7, 22, 57, 84, 94, 154, 195, 239, 289, 292, 306, 320, 325, 357, 371] [8, 23, 58, 85, 95, 155, 196, 240, 290, 293, 307, 321, 326, 358, 372] [9, 24, 59, 86, 96, 156, 197, 241, 291, 294, 308, 322, 327, 359, 373] [10, 25, 60, 87, 97, 157, 198, 242, 292, 295, 309, 323, 328, 360, 374] [11, 26, 61, 88, 98, 158, 199, 243, 293, 296, 310, 324, 329, 361, 375] [12, 27, 62, 89, 99, 159, 200, 244, 294, 297, 311, 325, 330, 362, 376] [13, 28, 63, 90, 100, 160, 201, 245, 295, 298, 312, 326, 331, 363, 377] [14, 29, 64, 91, 101, 161, 189, 202, 246, 296, 299, 313, 327, 332, 364] [15, 30, 65, 92, 102, 162, 190, 203, 247, 297, 300, 314, 328, 333, 365] [16, 31, 66, 93, 103, 163, 191, 204, 248, 298, 301, 315, 329, 334, 366] [17, 32, 67, 94, 104, 164, 192, 205, 249, 299, 302, 316, 330, 335, 367] [18, 33, 68, 95, 105, 165, 193, 206, 250, 300, 303, 317, 331, 336, 368] [19, 34, 69, 96, 106, 166, 194, 207, 251, 301, 304, 318, 332, 337, 369] [20, 35, 70, 97, 107, 167, 195, 208, 252, 302, 305, 319, 333, 338, 370] [21, 36, 71, 98, 108, 168, 196, 209, 253, 303, 306, 320, 334, 339, 371] [22, 37, 72, 99, 109, 169, 197, 210, 254, 304, 307, 321, 335, 340, 372] [23, 38, 73, 100, 110, 170, 198, 211, 255, 305, 308, 322, 336, 341, 373] [24, 39, 74, 101, 111, 171, 199, 212, 256, 306, 309, 323, 337, 342, 374] [25, 40, 75, 102, 112, 172, 200, 213, 257, 307, 310, 324, 338, 343, 375] [26, 41, 76, 103, 113, 173, 201, 214, 258, 308, 311, 325, 339, 344, 376] [27, 42, 77, 104, 114, 174, 202, 215, 259, 309, 312, 326, 340, 345, 377] [28, 43, 78, 105, 115, 175, 189, 203, 216, 260, 310, 313, 327, 341, 346] [29, 44, 79, 106, 116, 176, 190, 204, 217, 261, 311, 314, 328, 342, 347] [30, 45, 80, 107, 117, 177, 191, 205, 218, 262, 312, 315, 329, 343, 348] [31, 46, 81, 108, 118, 178, 192, 206, 219, 263, 313, 316, 330, 344, 349] [32, 47, 82, 109, 119, 179, 193, 207, 220, 264, 314, 317, 331, 345, 350] [33, 48, 83, 110, 120, 180, 194, 208, 221, 265, 315, 318, 332, 346, 351] [34, 49, 84, 111, 121, 181, 195, 209, 222, 266, 316, 319, 333, 347, 352] [35, 50, 85, 112, 122, 182, 196, 210, 223, 267, 317, 320, 334, 348, 353] [36, 51, 86, 113, 123, 183, 197, 211, 224, 268, 318, 321, 335, 349, 354] [37, 52, 87, 114, 124, 184, 198, 212, 225, 269, 319, 322, 336, 350, 355] [38, 53, 88, 115, 125, 185, 199, 213, 226, 270, 320, 323, 337, 351, 356] [39, 54, 89, 116, 126, 186, 200, 214, 227, 271, 321, 324, 338, 352, 357] [40, 55, 90, 117, 127, 187, 201, 215, 228, 272, 322, 325, 339, 353, 358] [41, 56, 91, 118, 128, 188, 202, 216, 229, 273, 323, 326, 340, 354, 359] [0, 42, 57, 92, 119, 129, 203, 217, 230, 274, 324, 327, 341, 355, 360] [1, 43, 58, 93, 120, 130, 204, 218, 231, 275, 325, 328, 342, 356, 361] [2, 44, 59, 94, 121, 131, 205, 219, 232, 276, 326, 329, 343, 357, 362] [3, 45, 60, 95, 122, 132, 206, 220, 233, 277, 327, 330, 344, 358, 363] [4, 46, 61, 96, 123, 133, 207, 221, 234, 278, 328, 331, 345, 359, 364] [5, 47, 62, 97, 124, 134, 208, 222, 235, 279, 329, 332, 346, 360, 365] [6, 48, 63, 98, 125, 135, 209, 223, 236, 280, 330, 333, 347, 361, 366] [7, 49, 64, 99, 126, 136, 210, 224, 237, 281, 331, 334, 348, 362, 367] [8, 50, 65, 100, 127, 137, 211, 225, 238, 282, 332, 335, 349, 363, 368] [9, 51, 66, 101, 128, 138, 212, 226, 239, 283, 333, 336, 350, 364, 369] [10, 52, 67, 102, 129, 139, 213, 227, 240, 284, 334, 337, 351, 365, 370] [11, 53, 68, 103, 130, 140, 214, 228, 241, 285, 335, 338, 352, 366, 371] [12, 54, 69, 104, 131, 141, 215, 229, 242, 286, 336, 339, 353, 367, 372] [13, 55, 70, 105, 132, 142, 216, 230, 243, 287, 337, 340, 354, 368, 373] [14, 56, 71, 106, 133, 143, 217, 231, 244, 288, 338, 341, 355, 369, 374] [15, 57, 72, 107, 134, 144, 218, 232, 245, 289, 339, 342, 356, 370, 375] [16, 58, 73, 108, 135, 145, 219, 233, 246, 290, 340, 343, 357, 371, 376] [17, 59, 74, 109, 136, 146, 220, 234, 247, 291, 341, 344, 358, 372, 377] [18, 60, 75, 110, 137, 147, 189, 221, 235, 248, 292, 342, 345, 359, 373] [19, 61, 76, 111, 138, 148, 190, 222, 236, 249, 293, 343, 346, 360, 374] [20, 62, 77, 112, 139, 149, 191, 223, 237, 250, 294, 344, 347, 361, 375] [21, 63, 78, 113, 140, 150, 192, 224, 238, 251, 295, 345, 348, 362, 376] [22, 64, 79, 114, 141, 151, 193, 225, 239, 252, 296, 346, 349, 363, 377] [23, 65, 80, 115, 142, 152, 189, 194, 226, 240, 253, 297, 347, 350, 364] [24, 66, 81, 116, 143, 153, 190, 195, 227, 241, 254, 298, 348, 351, 365] [25, 67, 82, 117, 144, 154, 191, 196, 228, 242, 255, 299, 349, 352, 366] [26, 68, 83, 118, 145, 155, 192, 197, 229, 243, 256, 300, 350, 353, 367] [27, 69, 84, 119, 146, 156, 193, 198, 230, 244, 257, 301, 351, 354, 368] [28, 70, 85, 120, 147, 157, 194, 199, 231, 245, 258, 302, 352, 355, 369] [29, 71, 86, 121, 148, 158, 195, 200, 232, 246, 259, 303, 353, 356, 370] [30, 72, 87, 122, 149, 159, 196, 201, 233, 247, 260, 304, 354, 357, 371] [31, 73, 88, 123, 150, 160, 197, 202, 234, 248, 261, 305, 355, 358, 372] [32, 74, 89, 124, 151, 161, 198, 203, 235, 249, 262, 306, 356, 359, 373] [33, 75, 90, 125, 152, 162, 199, 204, 236, 250, 263, 307, 357, 360, 374] [34, 76, 91, 126, 153, 163, 200, 205, 237, 251, 264, 308, 358, 361, 375] [35, 77, 92, 127, 154, 164, 201, 206, 238, 252, 265, 309, 359, 362, 376] [36, 78, 93, 128, 155, 165, 202, 207, 239, 253, 266, 310, 360, 363, 377] [37, 79, 94, 129, 156, 166, 189, 203, 208, 240, 254, 267, 311, 361, 364] [38, 80, 95, 130, 157, 167, 190, 204, 209, 241, 255, 268, 312, 362, 365] [39, 81, 96, 131, 158, 168, 191, 205, 210, 242, 256, 269, 313, 363, 366] [40, 82, 97, 132, 159, 169, 192, 206, 211, 243, 257, 270, 314, 364, 367] [41, 83, 98, 133, 160, 170, 193, 207, 212, 244, 258, 271, 315, 365, 368] [42, 84, 99, 134, 161, 171, 194, 208, 213, 245, 259, 272, 316, 366, 369] [43, 85, 100, 135, 162, 172, 195, 209, 214, 246, 260, 273, 317, 367, 370] [44, 86, 101, 136, 163, 173, 196, 210, 215, 247, 261, 274, 318, 368, 371] [45, 87, 102, 137, 164, 174, 197, 211, 216, 248, 262, 275, 319, 369, 372] [46, 88, 103, 138, 165, 175, 198, 212, 217, 249, 263, 276, 320, 370, 373] [47, 89, 104, 139, 166, 176, 199, 213, 218, 250, 264, 277, 321, 371, 374] [48, 90, 105, 140, 167, 177, 200, 214, 219, 251, 265, 278, 322, 372, 375] [49, 91, 106, 141, 168, 178, 201, 215, 220, 252, 266, 279, 323, 373, 376] [50, 92, 107, 142, 169, 179, 202, 216, 221, 253, 267, 280, 324, 374, 377] [51, 93, 108, 143, 170, 180, 189, 203, 217, 222, 254, 268, 281, 325, 375] [52, 94, 109, 144, 171, 181, 190, 204, 218, 223, 255, 269, 282, 326, 376] [53, 95, 110, 145, 172, 182, 191, 205, 219, 224, 256, 270, 283, 327, 377] [54, 96, 111, 146, 173, 183, 189, 192, 206, 220, 225, 257, 271, 284, 328] [55, 97, 112, 147, 174, 184, 190, 193, 207, 221, 226, 258, 272, 285, 329] [56, 98, 113, 148, 175, 185, 191, 194, 208, 222, 227, 259, 273, 286, 330] [57, 99, 114, 149, 176, 186, 192, 195, 209, 223, 228, 260, 274, 287, 331] [58, 100, 115, 150, 177, 187, 193, 196, 210, 224, 229, 261, 275, 288, 332] [59, 101, 116, 151, 178, 188, 194, 197, 211, 225, 230, 262, 276, 289, 333] [0, 60, 102, 117, 152, 179, 195, 198, 212, 226, 231, 263, 277, 290, 334] [1, 61, 103, 118, 153, 180, 196, 199, 213, 227, 232, 264, 278, 291, 335] [2, 62, 104, 119, 154, 181, 197, 200, 214, 228, 233, 265, 279, 292, 336] [3, 63, 105, 120, 155, 182, 198, 201, 215, 229, 234, 266, 280, 293, 337] [4, 64, 106, 121, 156, 183, 199, 202, 216, 230, 235, 267, 281, 294, 338] [5, 65, 107, 122, 157, 184, 200, 203, 217, 231, 236, 268, 282, 295, 339] [6, 66, 108, 123, 158, 185, 201, 204, 218, 232, 237, 269, 283, 296, 340] [7, 67, 109, 124, 159, 186, 202, 205, 219, 233, 238, 270, 284, 297, 341] [8, 68, 110, 125, 160, 187, 203, 206, 220, 234, 239, 271, 285, 298, 342] [9, 69, 111, 126, 161, 188, 204, 207, 221, 235, 240, 272, 286, 299, 343] [0, 10, 70, 112, 127, 162, 205, 208, 222, 236, 241, 273, 287, 300, 344] [1, 11, 71, 113, 128, 163, 206, 209, 223, 237, 242, 274, 288, 301, 345] [2, 12, 72, 114, 129, 164, 207, 210, 224, 238, 243, 275, 289, 302, 346] [3, 13, 73, 115, 130, 165, 208, 211, 225, 239, 244, 276, 290, 303, 347] [4, 14, 74, 116, 131, 166, 209, 212, 226, 240, 245, 277, 291, 304, 348] [5, 15, 75, 117, 132, 167, 210, 213, 227, 241, 246, 278, 292, 305, 349] [6, 16, 76, 118, 133, 168, 211, 214, 228, 242, 247, 279, 293, 306, 350] [7, 17, 77, 119, 134, 169, 212, 215, 229, 243, 248, 280, 294, 307, 351] [8, 18, 78, 120, 135, 170, 213, 216, 230, 244, 249, 281, 295, 308, 352] [9, 19, 79, 121, 136, 171, 214, 217, 231, 245, 250, 282, 296, 309, 353] [10, 20, 80, 122, 137, 172, 215, 218, 232, 246, 251, 283, 297, 310, 354] [11, 21, 81, 123, 138, 173, 216, 219, 233, 247, 252, 284, 298, 311, 355] [12, 22, 82, 124, 139, 174, 217, 220, 234, 248, 253, 285, 299, 312, 356] [13, 23, 83, 125, 140, 175, 218, 221, 235, 249, 254, 286, 300, 313, 357] [14, 24, 84, 126, 141, 176, 219, 222, 236, 250, 255, 287, 301, 314, 358] [15, 25, 85, 127, 142, 177, 220, 223, 237, 251, 256, 288, 302, 315, 359] [16, 26, 86, 128, 143, 178, 221, 224, 238, 252, 257, 289, 303, 316, 360] [17, 27, 87, 129, 144, 179, 222, 225, 239, 253, 258, 290, 304, 317, 361] [18, 28, 88, 130, 145, 180, 223, 226, 240, 254, 259, 291, 305, 318, 362] [19, 29, 89, 131, 146, 181, 224, 227, 241, 255, 260, 292, 306, 319, 363] [20, 30, 90, 132, 147, 182, 225, 228, 242, 256, 261, 293, 307, 320, 364] [21, 31, 91, 133, 148, 183, 226, 229, 243, 257, 262, 294, 308, 321, 365] [22, 32, 92, 134, 149, 184, 227, 230, 244, 258, 263, 295, 309, 322, 366] [23, 33, 93, 135, 150, 185, 228, 231, 245, 259, 264, 296, 310, 323, 367] [24, 34, 94, 136, 151, 186, 229, 232, 246, 260, 265, 297, 311, 324, 368] [25, 35, 95, 137, 152, 187, 230, 233, 247, 261, 266, 298, 312, 325, 369] [26, 36, 96, 138, 153, 188, 231, 234, 248, 262, 267, 299, 313, 326, 370] [0, 27, 37, 97, 139, 154, 232, 235, 249, 263, 268, 300, 314, 327, 371] [1, 28, 38, 98, 140, 155, 233, 236, 250, 264, 269, 301, 315, 328, 372] [2, 29, 39, 99, 141, 156, 234, 237, 251, 265, 270, 302, 316, 329, 373] [3, 30, 40, 100, 142, 157, 235, 238, 252, 266, 271, 303, 317, 330, 374] [4, 31, 41, 101, 143, 158, 236, 239, 253, 267, 272, 304, 318, 331, 375] [5, 32, 42, 102, 144, 159, 237, 240, 254, 268, 273, 305, 319, 332, 376] [6, 33, 43, 103, 145, 160, 238, 241, 255, 269, 274, 306, 320, 333, 377] [7, 34, 44, 104, 146, 161, 189, 239, 242, 256, 270, 275, 307, 321, 334] [8, 35, 45, 105, 147, 162, 190, 240, 243, 257, 271, 276, 308, 322, 335] [9, 36, 46, 106, 148, 163, 191, 241, 244, 258, 272, 277, 309, 323, 336] [10, 37, 47, 107, 149, 164, 192, 242, 245, 259, 273, 278, 310, 324, 337] [11, 38, 48, 108, 150, 165, 193, 243, 246, 260, 274, 279, 311, 325, 338] [12, 39, 49, 109, 151, 166, 194, 244, 247, 261, 275, 280, 312, 326, 339] [13, 40, 50, 110, 152, 167, 195, 245, 248, 262, 276, 281, 313, 327, 340] [14, 41, 51, 111, 153, 168, 196, 246, 249, 263, 277, 282, 314, 328, 341] [15, 42, 52, 112, 154, 169, 197, 247, 250, 264, 278, 283, 315, 329, 342]
Code ID 378-4-48 · download JSON · raw on GitHub