Best Known (18−9, 18, s)-Nets in Base 256
(18−9, 18, 16385)-Net over F256 — Constructive and digital
Digital (9, 18, 16385)-net over F256, using
- net defined by OOA [i] based on linear OOA(25618, 16385, F256, 9, 9) (dual of [(16385, 9), 147447, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(25618, 65541, F256, 9) (dual of [65541, 65523, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 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(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(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(25618, 65541, F256, 9) (dual of [65541, 65523, 10]-code), using
(18−9, 18, 31019)-Net over F256 — Digital
Digital (9, 18, 31019)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25618, 31019, F256, 2, 9) (dual of [(31019, 2), 62020, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25618, 32771, F256, 2, 9) (dual of [(32771, 2), 65524, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 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(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(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- OOA 2-folding [i] based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-code), using
- discarding factors / shortening the dual code based on linear OOA(25618, 32771, F256, 2, 9) (dual of [(32771, 2), 65524, 10]-NRT-code), using
(18−9, 18, large)-Net in Base 256 — Upper bound on s
There is no (9, 18, large)-net in base 256, because
- 7 times m-reduction [i] would yield (9, 11, large)-net in base 256, but