Best Known (27, 53, s)-Nets in Base 256
(27, 53, 5041)-Net over F256 — Constructive and digital
Digital (27, 53, 5041)-net over F256, using
- t-expansion [i] based on digital (26, 53, 5041)-net over F256, using
- net defined by OOA [i] based on linear OOA(25653, 5041, F256, 27, 27) (dual of [(5041, 27), 136054, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25653, 65534, F256, 27) (dual of [65534, 65481, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25653, 65534, F256, 27) (dual of [65534, 65481, 28]-code), using
- net defined by OOA [i] based on linear OOA(25653, 5041, F256, 27, 27) (dual of [(5041, 27), 136054, 28]-NRT-code), using
(27, 53, 14154)-Net over F256 — Digital
Digital (27, 53, 14154)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25653, 14154, F256, 4, 26) (dual of [(14154, 4), 56563, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25653, 16386, F256, 4, 26) (dual of [(16386, 4), 65491, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25653, 65544, F256, 26) (dual of [65544, 65491, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [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(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(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(25) ⊂ Ce(22) [i] based on
- OOA 4-folding [i] based on linear OA(25653, 65544, F256, 26) (dual of [65544, 65491, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(25653, 16386, F256, 4, 26) (dual of [(16386, 4), 65491, 27]-NRT-code), using
(27, 53, large)-Net in Base 256 — Upper bound on s
There is no (27, 53, large)-net in base 256, because
- 24 times m-reduction [i] would yield (27, 29, large)-net in base 256, but