Best Known (27, 27+11, s)-Nets in Base 256
(27, 27+11, 1710360)-Net over F256 — Constructive and digital
Digital (27, 38, 1710360)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- digital (20, 31, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- digital (2, 7, 32640)-net over F256, using
(27, 27+11, large)-Net over F256 — Digital
Digital (27, 38, large)-net over F256, using
- t-expansion [i] based on digital (26, 38, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25638, large, F256, 12) (dual of [large, large−38, 13]-code), using
- 4 times code embedding in larger space [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 4 times code embedding in larger space [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25638, large, F256, 12) (dual of [large, large−38, 13]-code), using
(27, 27+11, large)-Net in Base 256 — Upper bound on s
There is no (27, 38, large)-net in base 256, because
- 9 times m-reduction [i] would yield (27, 29, large)-net in base 256, but