Best Known (25, 25+19, s)-Nets in Base 256
(25, 25+19, 7284)-Net over F256 — Constructive and digital
Digital (25, 44, 7284)-net over F256, using
- net defined by OOA [i] based on linear OOA(25644, 7284, F256, 19, 19) (dual of [(7284, 19), 138352, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25644, 65557, F256, 19) (dual of [65557, 65513, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25644, 65560, F256, 19) (dual of [65560, 65516, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,5]) [i] based on
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to C([0,9]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25644, 65560, F256, 19) (dual of [65560, 65516, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25644, 65557, F256, 19) (dual of [65557, 65513, 20]-code), using
(25, 25+19, 34733)-Net over F256 — Digital
Digital (25, 44, 34733)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25644, 34733, F256, 19) (dual of [34733, 34689, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25644, 65560, F256, 19) (dual of [65560, 65516, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,5]) [i] based on
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to C([0,9]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25644, 65560, F256, 19) (dual of [65560, 65516, 20]-code), using
(25, 25+19, large)-Net in Base 256 — Upper bound on s
There is no (25, 44, large)-net in base 256, because
- 17 times m-reduction [i] would yield (25, 27, large)-net in base 256, but