Best Known (24, 47, s)-Nets in Base 256
(24, 47, 5958)-Net over F256 — Constructive and digital
Digital (24, 47, 5958)-net over F256, using
- 2561 times duplication [i] based on digital (23, 46, 5958)-net over F256, using
- net defined by OOA [i] based on linear OOA(25646, 5958, F256, 23, 23) (dual of [(5958, 23), 136988, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25646, 65539, F256, 23) (dual of [65539, 65493, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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([0,11]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25646, 65539, F256, 23) (dual of [65539, 65493, 24]-code), using
- net defined by OOA [i] based on linear OOA(25646, 5958, F256, 23, 23) (dual of [(5958, 23), 136988, 24]-NRT-code), using
(24, 47, 16386)-Net over F256 — Digital
Digital (24, 47, 16386)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25647, 16386, F256, 4, 23) (dual of [(16386, 4), 65497, 24]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25647, 65544, F256, 23) (dual of [65544, 65497, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- OOA 4-folding [i] based on linear OA(25647, 65544, F256, 23) (dual of [65544, 65497, 24]-code), using
(24, 47, large)-Net in Base 256 — Upper bound on s
There is no (24, 47, large)-net in base 256, because
- 21 times m-reduction [i] would yield (24, 26, large)-net in base 256, but