Best Known (56−18, 56, s)-Nets in Base 256
(56−18, 56, 932067)-Net over F256 — Constructive and digital
Digital (38, 56, 932067)-net over F256, using
- 2564 times duplication [i] based on digital (34, 52, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
(56−18, 56, 5062008)-Net over F256 — Digital
Digital (38, 56, 5062008)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25656, 5062008, F256, 18) (dual of [5062008, 5061952, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(25656, large, F256, 18) (dual of [large, large−56, 19]-code), using
- 4 times code embedding in larger space [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 4 times code embedding in larger space [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(25656, large, F256, 18) (dual of [large, large−56, 19]-code), using
(56−18, 56, large)-Net in Base 256 — Upper bound on s
There is no (38, 56, large)-net in base 256, because
- 16 times m-reduction [i] would yield (38, 40, large)-net in base 256, but