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[[180,36,8]] d ≤
n
180
k
36
d
8
kd²/n
12.8
w
9

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Distance

d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[1, 19, 23, 48, 49, 50, 68, 70]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[3, 8, 23, 27, 80, 92, 99, 102]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @yhu1996
provenance submitted through the challenge
novelty novelty not audited
construction Mitten lifted product LP(A,B) (Bhardwaj et al arXiv:2607.28795, Def.4/8) on non-abelian group D18 (order 36): a0=[16, 18, 27], a1=[0, 16, 30], b0=[24, 27, 34], b1=[0, 8, 19] over F2[G]. n=5|G|, k=|G|, weight-9.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2607.28795
date 2026-08-04
notes Found with Jukebox
family lifted product (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 72 · Z-checks 72
H_X (72 checks, sparse supports)
[16, 27, 29, 72, 88, 102, 168, 171, 178] [20, 23, 25, 73, 92, 106, 164, 175, 177] [21, 22, 24, 74, 93, 107, 162, 175, 177] [19, 21, 24, 75, 96, 105, 160, 173, 179] [18, 20, 25, 76, 97, 104, 166, 173, 179] [17, 26, 28, 77, 89, 103, 158, 171, 178] [15, 17, 28, 78, 100, 101, 156, 169, 176] [14, 16, 29, 79, 100, 101, 169, 170, 176] [13, 30, 32, 80, 85, 99, 154, 167, 174] [12, 31, 33, 81, 84, 98, 167, 172, 174] [11, 13, 32, 82, 97, 104, 152, 165, 172] [10, 12, 33, 83, 96, 105, 165, 172, 174] [9, 34, 35, 81, 84, 95, 150, 163, 170] [8, 34, 35, 80, 85, 94, 163, 170, 176] [7, 9, 35, 86, 93, 107, 149, 161, 168] [6, 8, 34, 87, 92, 106, 161, 168, 178] [0, 31, 33, 72, 88, 91, 147, 159, 166] [5, 30, 32, 77, 89, 90, 159, 166, 179] [0, 4, 31, 89, 90, 103, 146, 157, 164] [3, 5, 30, 88, 91, 102, 157, 164, 177] [1, 27, 29, 73, 87, 92, 145, 155, 162] [2, 26, 28, 74, 86, 93, 155, 162, 175] [1, 2, 27, 85, 94, 99, 148, 153, 160] [1, 2, 26, 84, 95, 98, 153, 160, 173] [3, 23, 25, 75, 83, 96, 144, 151, 158] [4, 22, 24, 76, 82, 97, 151, 158, 171] [3, 5, 23, 81, 95, 98, 144, 151, 156] [0, 4, 22, 80, 94, 99, 144, 156, 169] [6, 19, 21, 78, 79, 100, 148, 153, 154] [7, 18, 20, 78, 79, 101, 148, 154, 167] [6, 8, 19, 72, 91, 102, 145, 152, 155] [7, 9, 18, 77, 90, 103, 145, 152, 165] [10, 15, 17, 76, 82, 104, 146, 150, 157] [11, 14, 16, 75, 83, 105, 146, 150, 163] [10, 12, 15, 73, 87, 106, 147, 149, 159] [11, 13, 14, 74, 86, 107, 147, 149, 161] [52, 63, 65, 108, 124, 138, 144, 152, 163] [56, 59, 61, 109, 128, 142, 145, 149, 167] [57, 58, 60, 110, 129, 143, 146, 147, 169] [55, 57, 60, 111, 132, 141, 146, 147, 171] [54, 56, 61, 112, 133, 140, 148, 150, 165] [53, 62, 64, 113, 125, 139, 145, 149, 173] [51, 53, 64, 114, 136, 137, 148, 150, 175] [50, 52, 65, 115, 136, 137, 151, 154, 161] [49, 66, 68, 116, 121, 135, 144, 152, 177] [48, 67, 69, 117, 120, 134, 153, 156, 159] [47, 49, 68, 118, 133, 140, 151, 154, 179] [46, 48, 69, 119, 132, 141, 155, 157, 158] [45, 70, 71, 117, 120, 131, 153, 156, 178] [44, 70, 71, 116, 121, 130, 155, 157, 160] [43, 45, 71, 122, 129, 143, 155, 158, 176] [42, 44, 70, 123, 128, 142, 153, 159, 162] [36, 67, 69, 108, 124, 127, 157, 160, 174] [41, 66, 68, 113, 125, 126, 151, 161, 164] [36, 40, 67, 125, 126, 139, 159, 162, 172] [39, 41, 66, 124, 127, 138, 144, 163, 166] [37, 63, 65, 109, 123, 128, 161, 164, 170] [38, 62, 64, 110, 122, 129, 148, 165, 168] [37, 38, 63, 121, 130, 135, 163, 166, 168] [37, 38, 62, 120, 131, 134, 145, 167, 170] [39, 59, 61, 111, 119, 132, 165, 166, 168] [40, 58, 60, 112, 118, 133, 146, 169, 172] [39, 41, 59, 117, 131, 134, 164, 167, 170] [36, 40, 58, 116, 130, 135, 147, 171, 174] [42, 55, 57, 114, 115, 136, 162, 169, 172] [43, 54, 56, 114, 115, 137, 149, 173, 176] [42, 44, 55, 108, 127, 138, 160, 171, 174] [43, 45, 54, 113, 126, 139, 150, 175, 178] [46, 51, 53, 112, 118, 140, 158, 173, 176] [47, 50, 52, 111, 119, 141, 152, 177, 179] [46, 48, 51, 109, 123, 142, 156, 175, 178] [47, 49, 50, 110, 122, 143, 154, 177, 179]
H_Z (72 checks, sparse supports)
[24, 26, 27, 36, 44, 55, 160, 162, 171] [20, 30, 31, 37, 41, 59, 164, 166, 167] [18, 32, 33, 38, 39, 61, 165, 166, 167] [16, 34, 35, 38, 39, 63, 163, 168, 170] [22, 28, 29, 40, 42, 57, 162, 169, 171] [14, 34, 35, 37, 41, 65, 161, 163, 170] [12, 32, 33, 40, 42, 67, 159, 172, 174] [24, 25, 26, 43, 46, 53, 158, 173, 175] [10, 30, 31, 36, 44, 69, 157, 159, 174] [22, 23, 28, 45, 48, 51, 156, 158, 175] [8, 28, 29, 43, 46, 71, 155, 176, 178] [20, 21, 30, 47, 49, 50, 154, 177, 179] [6, 26, 27, 45, 48, 70, 153, 155, 178] [18, 19, 32, 47, 49, 52, 152, 154, 179] [5, 24, 25, 47, 50, 68, 151, 177, 179] [16, 17, 34, 45, 51, 54, 150, 176, 178] [3, 22, 23, 49, 52, 66, 144, 151, 177] [14, 15, 35, 43, 53, 56, 149, 150, 176] [2, 20, 21, 51, 54, 64, 148, 173, 175] [12, 13, 33, 36, 55, 58, 147, 172, 174] [1, 18, 19, 53, 56, 62, 145, 148, 173] [10, 11, 31, 40, 57, 60, 146, 147, 172] [4, 16, 17, 55, 58, 60, 146, 169, 171] [8, 9, 29, 37, 59, 62, 145, 168, 170] [0, 14, 15, 57, 58, 60, 146, 147, 169] [6, 7, 27, 38, 61, 64, 145, 148, 168] [7, 12, 13, 56, 59, 62, 149, 165, 167] [0, 5, 25, 39, 63, 66, 144, 164, 166] [9, 10, 11, 54, 61, 64, 149, 150, 165] [3, 4, 23, 41, 65, 68, 144, 151, 164] [8, 9, 11, 52, 63, 66, 152, 161, 163] [1, 2, 21, 42, 67, 70, 153, 160, 162] [6, 7, 13, 50, 65, 68, 152, 154, 161] [1, 2, 19, 44, 69, 71, 153, 155, 160] [0, 5, 15, 48, 67, 70, 156, 157, 159] [3, 4, 17, 46, 69, 71, 156, 157, 158] [96, 98, 99, 108, 116, 127, 144, 160, 174] [92, 102, 103, 109, 113, 131, 145, 164, 178] [90, 104, 105, 110, 111, 133, 146, 165, 179] [88, 106, 107, 110, 111, 135, 147, 168, 177] [94, 100, 101, 112, 114, 129, 148, 169, 176] [86, 106, 107, 109, 113, 137, 149, 161, 175] [84, 104, 105, 112, 114, 139, 150, 172, 173] [96, 97, 98, 115, 118, 125, 151, 172, 173] [82, 102, 103, 108, 116, 141, 152, 157, 171] [94, 95, 100, 117, 120, 123, 153, 156, 170] [80, 100, 101, 115, 118, 143, 154, 169, 176] [92, 93, 102, 119, 121, 122, 155, 168, 177] [78, 98, 99, 117, 120, 142, 153, 156, 167] [90, 91, 104, 119, 121, 124, 152, 157, 166] [77, 96, 97, 119, 122, 140, 158, 165, 179] [88, 89, 106, 117, 123, 126, 159, 164, 178] [75, 94, 95, 121, 124, 138, 144, 160, 163] [86, 87, 107, 115, 125, 128, 149, 161, 162] [74, 92, 93, 123, 126, 136, 161, 162, 175] [84, 85, 105, 108, 127, 130, 160, 163, 174] [73, 90, 91, 125, 128, 134, 145, 159, 164] [82, 83, 103, 112, 129, 132, 146, 158, 165] [76, 88, 89, 127, 130, 132, 157, 166, 171] [80, 81, 101, 109, 131, 134, 156, 167, 170] [72, 86, 87, 129, 130, 132, 147, 155, 168] [78, 79, 99, 110, 133, 136, 148, 154, 169] [79, 84, 85, 128, 131, 134, 153, 167, 170] [72, 77, 97, 111, 135, 138, 152, 166, 171] [81, 82, 83, 126, 133, 136, 150, 151, 172] [75, 76, 95, 113, 137, 140, 150, 151, 173] [80, 81, 83, 124, 135, 138, 144, 163, 174] [73, 74, 93, 114, 139, 142, 149, 162, 175] [78, 79, 85, 122, 137, 140, 148, 154, 176] [73, 74, 91, 116, 141, 143, 147, 155, 177] [72, 77, 87, 120, 139, 142, 145, 159, 178] [75, 76, 89, 118, 141, 143, 146, 158, 179]
raw submission JSON