Best Known (53−21, 53, s)-Nets in Base 256
(53−21, 53, 6812)-Net over F256 — Constructive and digital
Digital (32, 53, 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 (20, 41, 6553)-net over F256, using
- net defined by OOA [i] based on linear OOA(25641, 6553, F256, 21, 21) (dual of [(6553, 21), 137572, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25641, 65531, F256, 21) (dual of [65531, 65490, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25641, 65531, F256, 21) (dual of [65531, 65490, 22]-code), using
- net defined by OOA [i] based on linear OOA(25641, 6553, F256, 21, 21) (dual of [(6553, 21), 137572, 22]-NRT-code), using
- digital (2, 12, 259)-net over F256, using
(53−21, 53, 78462)-Net over F256 — Digital
Digital (32, 53, 78462)-net over F256, using
(53−21, 53, large)-Net in Base 256 — Upper bound on s
There is no (32, 53, large)-net in base 256, because
- 19 times m-reduction [i] would yield (32, 34, large)-net in base 256, but