Best Known (56−16, 56, s)-Nets in Base 256
(56−16, 56, 1048834)-Net over F256 — Constructive and digital
Digital (40, 56, 1048834)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (30, 46, 1048575)-net over F256, using
- net defined by OOA [i] based on linear OOA(25646, 1048575, F256, 16, 16) (dual of [(1048575, 16), 16777154, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(25646, 8388600, F256, 16) (dual of [8388600, 8388554, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(25646, 8388600, F256, 16) (dual of [8388600, 8388554, 17]-code), using
- net defined by OOA [i] based on linear OOA(25646, 1048575, F256, 16, 16) (dual of [(1048575, 16), 16777154, 17]-NRT-code), using
- digital (2, 10, 259)-net over F256, using
(56−16, 56, large)-Net over F256 — Digital
Digital (40, 56, large)-net over F256, using
- 2 times m-reduction [i] based on digital (40, 58, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25658, large, F256, 18) (dual of [large, large−58, 19]-code), using
- strength reduction [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- strength reduction [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25658, large, F256, 18) (dual of [large, large−58, 19]-code), using
(56−16, 56, large)-Net in Base 256 — Upper bound on s
There is no (40, 56, large)-net in base 256, because
- 14 times m-reduction [i] would yield (40, 42, large)-net in base 256, but