Best Known (65−15, 65, s)-Nets in Base 256
(65−15, 65, 2396742)-Net over F256 — Constructive and digital
Digital (50, 65, 2396742)-net over F256, using
- 2563 times duplication [i] based on digital (47, 62, 2396742)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (12, 19, 2796200)-net over F256, using
- net defined by OOA [i] based on linear OOA(25619, 2796200, F256, 7, 7) (dual of [(2796200, 7), 19573381, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25619, 2796200, F256, 6, 7) (dual of [(2796200, 6), 16777181, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(25619, 8388601, F256, 7) (dual of [8388601, 8388582, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(25619, 8388601, F256, 7) (dual of [8388601, 8388582, 8]-code), using
- appending kth column [i] based on linear OOA(25619, 2796200, F256, 6, 7) (dual of [(2796200, 6), 16777181, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(25619, 2796200, F256, 7, 7) (dual of [(2796200, 7), 19573381, 8]-NRT-code), 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 (12, 19, 2796200)-net over F256, using
- (u, u+v)-construction [i] based on
(65−15, 65, large)-Net over F256 — Digital
Digital (50, 65, large)-net over F256, using
- t-expansion [i] based on digital (47, 65, large)-net over F256, using
- 3 times m-reduction [i] based on digital (47, 68, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25668, large, F256, 21) (dual of [large, large−68, 22]-code), using
- 7 times code embedding in larger space [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]
- 7 times code embedding in larger space [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(25668, large, F256, 21) (dual of [large, large−68, 22]-code), using
- 3 times m-reduction [i] based on digital (47, 68, large)-net over F256, using
(65−15, 65, large)-Net in Base 256 — Upper bound on s
There is no (50, 65, large)-net in base 256, because
- 13 times m-reduction [i] would yield (50, 52, large)-net in base 256, but