Best Known (39, 39+19, s)-Nets in Base 256
(39, 39+19, 932067)-Net over F256 — Constructive and digital
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
(39, 39+19, 4194302)-Net over F256 — Digital
Digital (39, 58, 4194302)-net over F256, using
- 2561 times duplication [i] based on digital (38, 57, 4194302)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25657, 4194302, F256, 2, 19) (dual of [(4194302, 2), 8388547, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25655, 4194301, F256, 2, 19) (dual of [(4194301, 2), 8388547, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25655, 8388602, F256, 19) (dual of [8388602, 8388547, 20]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- OOA 2-folding [i] based on linear OA(25655, 8388602, F256, 19) (dual of [8388602, 8388547, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25655, 4194301, F256, 2, 19) (dual of [(4194301, 2), 8388547, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25657, 4194302, F256, 2, 19) (dual of [(4194302, 2), 8388547, 20]-NRT-code), using
(39, 39+19, large)-Net in Base 256 — Upper bound on s
There is no (39, 58, large)-net in base 256, because
- 17 times m-reduction [i] would yield (39, 41, large)-net in base 256, but