Best Known (19, 27, s)-Nets in Base 256
(19, 27, 2097408)-Net over F256 — Constructive and digital
Digital (19, 27, 2097408)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (14, 22, 2097150)-net over F256, using
- net defined by OOA [i] based on linear OOA(25622, 2097150, F256, 8, 8) (dual of [(2097150, 8), 16777178, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(25622, 8388600, F256, 8) (dual of [8388600, 8388578, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(25622, 8388600, F256, 8) (dual of [8388600, 8388578, 9]-code), using
- net defined by OOA [i] based on linear OOA(25622, 2097150, F256, 8, 8) (dual of [(2097150, 8), 16777178, 9]-NRT-code), using
- digital (1, 5, 258)-net over F256, using
(19, 27, large)-Net over F256 — Digital
Digital (19, 27, large)-net over F256, using
- t-expansion [i] based on digital (18, 27, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25627, large, F256, 9) (dual of [large, large−27, 10]-code), using
- 2 times code embedding in larger space [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 2 times code embedding in larger space [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25627, large, F256, 9) (dual of [large, large−27, 10]-code), using
(19, 27, large)-Net in Base 256 — Upper bound on s
There is no (19, 27, large)-net in base 256, because
- 6 times m-reduction [i] would yield (19, 21, large)-net in base 256, but