Best Known (52−15, 52, s)-Nets in Base 256
(52−15, 52, 1198630)-Net over F256 — Constructive and digital
Digital (37, 52, 1198630)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- 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
- digital (2, 9, 259)-net over F256, using
(52−15, 52, large)-Net over F256 — Digital
Digital (37, 52, large)-net over F256, using
- 2561 times duplication [i] based on digital (36, 51, large)-net over F256, using
- t-expansion [i] based on digital (35, 51, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25651, large, F256, 16) (dual of [large, large−51, 17]-code), using
- 5 times code embedding in larger space [i] 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]
- 5 times code embedding in larger space [i] based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25651, large, F256, 16) (dual of [large, large−51, 17]-code), using
- t-expansion [i] based on digital (35, 51, large)-net over F256, using
(52−15, 52, large)-Net in Base 256 — Upper bound on s
There is no (37, 52, large)-net in base 256, because
- 13 times m-reduction [i] would yield (37, 39, large)-net in base 256, but