Best Known (40, 59, s)-Nets in Base 256
(40, 59, 932067)-Net over F256 — Constructive and digital
Digital (40, 59, 932067)-net over F256, using
- 2561 times duplication [i] based on digital (39, 58, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25658, 932067, F256, 21, 19) (dual of [(932067, 21), 19573349, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(25658, 2796202, F256, 3, 19) (dual of [(2796202, 3), 8388548, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25655, 2796201, F256, 3, 19) (dual of [(2796201, 3), 8388548, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- OOA 3-folding [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25655, 2796201, F256, 3, 19) (dual of [(2796201, 3), 8388548, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(25658, 2796202, F256, 3, 19) (dual of [(2796202, 3), 8388548, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(25658, 932067, F256, 21, 19) (dual of [(932067, 21), 19573349, 20]-NRT-code), using
(40, 59, 4631828)-Net over F256 — Digital
Digital (40, 59, 4631828)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25659, 4631828, F256, 19) (dual of [4631828, 4631769, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25659, large, F256, 19) (dual of [large, large−59, 20]-code), using
- 4 times code embedding in larger space [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 4 times code embedding in larger space [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25659, large, F256, 19) (dual of [large, large−59, 20]-code), using
(40, 59, large)-Net in Base 256 — Upper bound on s
There is no (40, 59, large)-net in base 256, because
- 17 times m-reduction [i] would yield (40, 42, large)-net in base 256, but