Best Known (17, 17+13, s)-Nets in Base 256
(17, 17+13, 10925)-Net over F256 — Constructive and digital
Digital (17, 30, 10925)-net over F256, using
- net defined by OOA [i] based on linear OOA(25630, 10925, F256, 13, 13) (dual of [(10925, 13), 141995, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25630, 65551, F256, 13) (dual of [65551, 65521, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25630, 65554, F256, 13) (dual of [65554, 65524, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,3]) [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(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(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to C([0,6]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25630, 65554, F256, 13) (dual of [65554, 65524, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25630, 65551, F256, 13) (dual of [65551, 65521, 14]-code), using
(17, 17+13, 42996)-Net over F256 — Digital
Digital (17, 30, 42996)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25630, 42996, F256, 13) (dual of [42996, 42966, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25630, 65554, F256, 13) (dual of [65554, 65524, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,3]) [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(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(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to C([0,6]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25630, 65554, F256, 13) (dual of [65554, 65524, 14]-code), using
(17, 17+13, large)-Net in Base 256 — Upper bound on s
There is no (17, 30, large)-net in base 256, because
- 11 times m-reduction [i] would yield (17, 19, large)-net in base 256, but