Best Known (67−27, 67, s)-Nets in Base 256
(67−27, 67, 5299)-Net over F256 — Constructive and digital
Digital (40, 67, 5299)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (26, 53, 5041)-net over F256, using
- net defined by OOA [i] based on linear OOA(25653, 5041, F256, 27, 27) (dual of [(5041, 27), 136054, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25653, 65534, F256, 27) (dual of [65534, 65481, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25653, 65534, F256, 27) (dual of [65534, 65481, 28]-code), using
- net defined by OOA [i] based on linear OOA(25653, 5041, F256, 27, 27) (dual of [(5041, 27), 136054, 28]-NRT-code), using
- digital (1, 14, 258)-net over F256, using
(67−27, 67, 66479)-Net over F256 — Digital
Digital (40, 67, 66479)-net over F256, using
(67−27, 67, large)-Net in Base 256 — Upper bound on s
There is no (40, 67, large)-net in base 256, because
- 25 times m-reduction [i] would yield (40, 42, large)-net in base 256, but