Best Known (15, 28, s)-Nets in Base 256
(15, 28, 10924)-Net over F256 — Constructive and digital
Digital (15, 28, 10924)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 10924, F256, 13, 13) (dual of [(10924, 13), 141984, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25628, 65545, F256, 13) (dual of [65545, 65517, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, 65548, F256, 13) (dual of [65548, 65520, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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([0,6]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25628, 65548, F256, 13) (dual of [65548, 65520, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25628, 65545, F256, 13) (dual of [65545, 65517, 14]-code), using
(15, 28, 32419)-Net over F256 — Digital
Digital (15, 28, 32419)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25628, 32419, F256, 2, 13) (dual of [(32419, 2), 64810, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25628, 32774, F256, 2, 13) (dual of [(32774, 2), 65520, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25628, 65548, F256, 13) (dual of [65548, 65520, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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([0,6]) ⊂ C([0,4]) [i] based on
- OOA 2-folding [i] based on linear OA(25628, 65548, F256, 13) (dual of [65548, 65520, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(25628, 32774, F256, 2, 13) (dual of [(32774, 2), 65520, 14]-NRT-code), using
(15, 28, large)-Net in Base 256 — Upper bound on s
There is no (15, 28, large)-net in base 256, because
- 11 times m-reduction [i] would yield (15, 17, large)-net in base 256, but