Best Known (30, 54, s)-Nets in Base 256
(30, 54, 5463)-Net over F256 — Constructive and digital
Digital (30, 54, 5463)-net over F256, using
- 2561 times duplication [i] based on digital (29, 53, 5463)-net over F256, using
- net defined by OOA [i] based on linear OOA(25653, 5463, F256, 24, 24) (dual of [(5463, 24), 131059, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(25653, 65556, F256, 24) (dual of [65556, 65503, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [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(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2566, 20, F256, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- Reed–Solomon code RS(250,256) [i]
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- OA 12-folding and stacking [i] based on linear OA(25653, 65556, F256, 24) (dual of [65556, 65503, 25]-code), using
- net defined by OOA [i] based on linear OOA(25653, 5463, F256, 24, 24) (dual of [(5463, 24), 131059, 25]-NRT-code), using
(30, 54, 31267)-Net over F256 — Digital
Digital (30, 54, 31267)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25654, 31267, F256, 2, 24) (dual of [(31267, 2), 62480, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25654, 32779, F256, 2, 24) (dual of [(32779, 2), 65504, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25654, 65558, F256, 24) (dual of [65558, 65504, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(25654, 65559, F256, 24) (dual of [65559, 65505, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [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(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(25654, 65559, F256, 24) (dual of [65559, 65505, 25]-code), using
- OOA 2-folding [i] based on linear OA(25654, 65558, F256, 24) (dual of [65558, 65504, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(25654, 32779, F256, 2, 24) (dual of [(32779, 2), 65504, 25]-NRT-code), using
(30, 54, large)-Net in Base 256 — Upper bound on s
There is no (30, 54, large)-net in base 256, because
- 22 times m-reduction [i] would yield (30, 32, large)-net in base 256, but