Best Known (45−15, 45, s)-Nets in Base 256
(45−15, 45, 1198371)-Net over F256 — Constructive and digital
Digital (30, 45, 1198371)-net over F256, using
- 2562 times duplication [i] based on digital (28, 43, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
(45−15, 45, 4194302)-Net over F256 — Digital
Digital (30, 45, 4194302)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25645, 4194302, F256, 2, 15) (dual of [(4194302, 2), 8388559, 16]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25643, 4194301, F256, 2, 15) (dual of [(4194301, 2), 8388559, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25643, 8388602, F256, 15) (dual of [8388602, 8388559, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 2-folding [i] based on linear OA(25643, 8388602, F256, 15) (dual of [8388602, 8388559, 16]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25643, 4194301, F256, 2, 15) (dual of [(4194301, 2), 8388559, 16]-NRT-code), using
(45−15, 45, large)-Net in Base 256 — Upper bound on s
There is no (30, 45, large)-net in base 256, because
- 13 times m-reduction [i] would yield (30, 32, large)-net in base 256, but