Best Known (61−24, 61, s)-Nets in Base 256
(61−24, 61, 5720)-Net over F256 — Constructive and digital
Digital (37, 61, 5720)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 14, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (23, 47, 5461)-net over F256, using
- net defined by OOA [i] based on linear OOA(25647, 5461, F256, 24, 24) (dual of [(5461, 24), 131017, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(25647, 65532, F256, 24) (dual of [65532, 65485, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(25647, 65532, F256, 24) (dual of [65532, 65485, 25]-code), using
- net defined by OOA [i] based on linear OOA(25647, 5461, F256, 24, 24) (dual of [(5461, 24), 131017, 25]-NRT-code), using
- digital (2, 14, 259)-net over F256, using
(61−24, 61, 90166)-Net over F256 — Digital
Digital (37, 61, 90166)-net over F256, using
(61−24, 61, large)-Net in Base 256 — Upper bound on s
There is no (37, 61, large)-net in base 256, because
- 22 times m-reduction [i] would yield (37, 39, large)-net in base 256, but