Best Known (51−20, 51, s)-Nets in Base 256
(51−20, 51, 6812)-Net over F256 — Constructive and digital
Digital (31, 51, 6812)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (19, 39, 6553)-net over F256, using
- net defined by OOA [i] based on linear OOA(25639, 6553, F256, 20, 20) (dual of [(6553, 20), 131021, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(25639, 65530, F256, 20) (dual of [65530, 65491, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(25639, 65530, F256, 20) (dual of [65530, 65491, 21]-code), using
- net defined by OOA [i] based on linear OOA(25639, 6553, F256, 20, 20) (dual of [(6553, 20), 131021, 21]-NRT-code), using
- digital (2, 12, 259)-net over F256, using
(51−20, 51, 90562)-Net over F256 — Digital
Digital (31, 51, 90562)-net over F256, using
(51−20, 51, large)-Net in Base 256 — Upper bound on s
There is no (31, 51, large)-net in base 256, because
- 18 times m-reduction [i] would yield (31, 33, large)-net in base 256, but