Best Known (19, 38, s)-Nets in Base 128
(19, 38, 1821)-Net over F128 — Constructive and digital
Digital (19, 38, 1821)-net over F128, using
- net defined by OOA [i] based on linear OOA(12838, 1821, F128, 19, 19) (dual of [(1821, 19), 34561, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(12838, 16390, F128, 19) (dual of [16390, 16352, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- OOA 9-folding and stacking with additional row [i] based on linear OA(12838, 16390, F128, 19) (dual of [16390, 16352, 20]-code), using
(19, 38, 4170)-Net over F128 — Digital
Digital (19, 38, 4170)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12838, 4170, F128, 3, 19) (dual of [(4170, 3), 12472, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12838, 5463, F128, 3, 19) (dual of [(5463, 3), 16351, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12838, 16389, F128, 19) (dual of [16389, 16351, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(12838, 16390, F128, 19) (dual of [16390, 16352, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12838, 16390, F128, 19) (dual of [16390, 16352, 20]-code), using
- OOA 3-folding [i] based on linear OA(12838, 16389, F128, 19) (dual of [16389, 16351, 20]-code), using
- discarding factors / shortening the dual code based on linear OOA(12838, 5463, F128, 3, 19) (dual of [(5463, 3), 16351, 20]-NRT-code), using
(19, 38, large)-Net in Base 128 — Upper bound on s
There is no (19, 38, large)-net in base 128, because
- 17 times m-reduction [i] would yield (19, 21, large)-net in base 128, but