Best Known (57−24, 57, s)-Nets in Base 256
(57−24, 57, 5464)-Net over F256 — Constructive and digital
Digital (33, 57, 5464)-net over F256, using
- net defined by OOA [i] based on linear OOA(25657, 5464, F256, 24, 24) (dual of [(5464, 24), 131079, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(25657, 65568, F256, 24) (dual of [65568, 65511, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(12) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25610, 32, F256, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,256)), using
- discarding factors / shortening the dual code based on linear OA(25610, 256, F256, 10) (dual of [256, 246, 11]-code or 256-arc in PG(9,256)), using
- Reed–Solomon code RS(246,256) [i]
- discarding factors / shortening the dual code based on linear OA(25610, 256, F256, 10) (dual of [256, 246, 11]-code or 256-arc in PG(9,256)), using
- construction X applied to Ce(23) ⊂ Ce(12) [i] based on
- OA 12-folding and stacking [i] based on linear OA(25657, 65568, F256, 24) (dual of [65568, 65511, 25]-code), using
(57−24, 57, 47895)-Net over F256 — Digital
Digital (33, 57, 47895)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25657, 47895, F256, 24) (dual of [47895, 47838, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(25657, 65568, F256, 24) (dual of [65568, 65511, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(12) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25610, 32, F256, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,256)), using
- discarding factors / shortening the dual code based on linear OA(25610, 256, F256, 10) (dual of [256, 246, 11]-code or 256-arc in PG(9,256)), using
- Reed–Solomon code RS(246,256) [i]
- discarding factors / shortening the dual code based on linear OA(25610, 256, F256, 10) (dual of [256, 246, 11]-code or 256-arc in PG(9,256)), using
- construction X applied to Ce(23) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(25657, 65568, F256, 24) (dual of [65568, 65511, 25]-code), using
(57−24, 57, large)-Net in Base 256 — Upper bound on s
There is no (33, 57, large)-net in base 256, because
- 22 times m-reduction [i] would yield (33, 35, large)-net in base 256, but