Best Known (32, 32+26, s)-Nets in Base 256
(32, 32+26, 5043)-Net over F256 — Constructive and digital
Digital (32, 58, 5043)-net over F256, using
- net defined by OOA [i] based on linear OOA(25658, 5043, F256, 26, 26) (dual of [(5043, 26), 131060, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25658, 65559, F256, 26) (dual of [65559, 65501, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(25) ⊂ Ce(17) [i] based on
- OA 13-folding and stacking [i] based on linear OA(25658, 65559, F256, 26) (dual of [65559, 65501, 27]-code), using
(32, 32+26, 26995)-Net over F256 — Digital
Digital (32, 58, 26995)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25658, 26995, F256, 2, 26) (dual of [(26995, 2), 53932, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25658, 32779, F256, 2, 26) (dual of [(32779, 2), 65500, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25658, 65558, F256, 26) (dual of [65558, 65500, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25658, 65559, F256, 26) (dual of [65559, 65501, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(25) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(25658, 65559, F256, 26) (dual of [65559, 65501, 27]-code), using
- OOA 2-folding [i] based on linear OA(25658, 65558, F256, 26) (dual of [65558, 65500, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(25658, 32779, F256, 2, 26) (dual of [(32779, 2), 65500, 27]-NRT-code), using
(32, 32+26, large)-Net in Base 256 — Upper bound on s
There is no (32, 58, large)-net in base 256, because
- 24 times m-reduction [i] would yield (32, 34, large)-net in base 256, but