Best Known (13, 24, s)-Nets in Base 256
(13, 24, 13109)-Net over F256 — Constructive and digital
Digital (13, 24, 13109)-net over F256, using
- net defined by OOA [i] based on linear OOA(25624, 13109, F256, 11, 11) (dual of [(13109, 11), 144175, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25624, 65546, F256, 11) (dual of [65546, 65522, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(25624, 65548, F256, 11) (dual of [65548, 65524, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- 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(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25624, 65548, F256, 11) (dual of [65548, 65524, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25624, 65546, F256, 11) (dual of [65546, 65522, 12]-code), using
(13, 24, 32774)-Net over F256 — Digital
Digital (13, 24, 32774)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25624, 32774, F256, 2, 11) (dual of [(32774, 2), 65524, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25624, 65548, F256, 11) (dual of [65548, 65524, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- 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(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- OOA 2-folding [i] based on linear OA(25624, 65548, F256, 11) (dual of [65548, 65524, 12]-code), using
(13, 24, large)-Net in Base 256 — Upper bound on s
There is no (13, 24, large)-net in base 256, because
- 9 times m-reduction [i] would yield (13, 15, large)-net in base 256, but