Best Known (26, 52, s)-Nets in Base 256
(26, 52, 5041)-Net over F256 — Constructive and digital
Digital (26, 52, 5041)-net over F256, using
- 1 times m-reduction [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
(26, 52, 13108)-Net over F256 — Digital
Digital (26, 52, 13108)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25652, 13108, F256, 5, 26) (dual of [(13108, 5), 65488, 27]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25652, 65540, F256, 26) (dual of [65540, 65488, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25652, 65541, F256, 26) (dual of [65541, 65489, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [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(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(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(25652, 65541, F256, 26) (dual of [65541, 65489, 27]-code), using
- OOA 5-folding [i] based on linear OA(25652, 65540, F256, 26) (dual of [65540, 65488, 27]-code), using
(26, 52, large)-Net in Base 256 — Upper bound on s
There is no (26, 52, large)-net in base 256, because
- 24 times m-reduction [i] would yield (26, 28, large)-net in base 256, but