Best Known (43, 43+13, s)-Nets in Base 256
(43, 43+13, 2796201)-Net over F256 — Constructive and digital
Digital (43, 56, 2796201)-net over F256, using
- net defined by OOA [i] based on linear OOA(25656, 2796201, F256, 15, 13) (dual of [(2796201, 15), 41942959, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(25656, 5592403, F256, 3, 13) (dual of [(5592403, 3), 16777153, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25653, 5592402, F256, 3, 13) (dual of [(5592402, 3), 16777153, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25616, 2796201, F256, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- linear OOA(25637, 2796201, F256, 3, 13) (dual of [(2796201, 3), 8388566, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- OOA 3-folding [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- linear OOA(25616, 2796201, F256, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25653, 5592402, F256, 3, 13) (dual of [(5592402, 3), 16777153, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(25656, 5592403, F256, 3, 13) (dual of [(5592403, 3), 16777153, 14]-NRT-code), using
(43, 43+13, large)-Net over F256 — Digital
Digital (43, 56, large)-net over F256, using
- t-expansion [i] based on digital (42, 56, large)-net over F256, using
- 5 times m-reduction [i] based on digital (42, 61, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25661, large, F256, 19) (dual of [large, large−61, 20]-code), using
- strength reduction [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- strength reduction [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25661, large, F256, 19) (dual of [large, large−61, 20]-code), using
- 5 times m-reduction [i] based on digital (42, 61, large)-net over F256, using
(43, 43+13, large)-Net in Base 256 — Upper bound on s
There is no (43, 56, large)-net in base 256, because
- 11 times m-reduction [i] would yield (43, 45, large)-net in base 256, but