Best Known (53−23, 53, s)-Nets in Base 256
(53−23, 53, 5960)-Net over F256 — Constructive and digital
Digital (30, 53, 5960)-net over F256, using
- net defined by OOA [i] based on linear OOA(25653, 5960, F256, 23, 23) (dual of [(5960, 23), 137027, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25653, 65561, F256, 23) (dual of [65561, 65508, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25653, 65562, F256, 23) (dual of [65562, 65509, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(13) [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(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(22) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(25653, 65562, F256, 23) (dual of [65562, 65509, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25653, 65561, F256, 23) (dual of [65561, 65508, 24]-code), using
(53−23, 53, 32781)-Net over F256 — Digital
Digital (30, 53, 32781)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25653, 32781, F256, 2, 23) (dual of [(32781, 2), 65509, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25653, 65562, F256, 23) (dual of [65562, 65509, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(13) [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(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(22) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(25653, 65562, F256, 23) (dual of [65562, 65509, 24]-code), using
(53−23, 53, large)-Net in Base 256 — Upper bound on s
There is no (30, 53, large)-net in base 256, because
- 21 times m-reduction [i] would yield (30, 32, large)-net in base 256, but