Best Known (33, 64, s)-Nets in Base 128
(33, 64, 1093)-Net over F128 — Constructive and digital
Digital (33, 64, 1093)-net over F128, using
- net defined by OOA [i] based on linear OOA(12864, 1093, F128, 31, 31) (dual of [(1093, 31), 33819, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12864, 16396, F128, 31) (dual of [16396, 16332, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- OOA 15-folding and stacking with additional row [i] based on linear OA(12864, 16396, F128, 31) (dual of [16396, 16332, 32]-code), using
(33, 64, 4946)-Net over F128 — Digital
Digital (33, 64, 4946)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12864, 4946, F128, 3, 31) (dual of [(4946, 3), 14774, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12864, 5465, F128, 3, 31) (dual of [(5465, 3), 16331, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12864, 16395, F128, 31) (dual of [16395, 16331, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 16396, F128, 31) (dual of [16396, 16332, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12864, 16396, F128, 31) (dual of [16396, 16332, 32]-code), using
- OOA 3-folding [i] based on linear OA(12864, 16395, F128, 31) (dual of [16395, 16331, 32]-code), using
- discarding factors / shortening the dual code based on linear OOA(12864, 5465, F128, 3, 31) (dual of [(5465, 3), 16331, 32]-NRT-code), using
(33, 64, large)-Net in Base 128 — Upper bound on s
There is no (33, 64, large)-net in base 128, because
- 29 times m-reduction [i] would yield (33, 35, large)-net in base 128, but