Best Known (22, 22+14, s)-Nets in Base 256
(22, 22+14, 9621)-Net over F256 — Constructive and digital
Digital (22, 36, 9621)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (13, 27, 9362)-net over F256, using
- net defined by OOA [i] based on linear OOA(25627, 9362, F256, 14, 14) (dual of [(9362, 14), 131041, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25627, 65534, F256, 14) (dual of [65534, 65507, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25627, 65534, F256, 14) (dual of [65534, 65507, 15]-code), using
- net defined by OOA [i] based on linear OOA(25627, 9362, F256, 14, 14) (dual of [(9362, 14), 131041, 15]-NRT-code), using
- digital (2, 9, 259)-net over F256, using
(22, 22+14, 103721)-Net over F256 — Digital
Digital (22, 36, 103721)-net over F256, using
(22, 22+14, large)-Net in Base 256 — Upper bound on s
There is no (22, 36, large)-net in base 256, because
- 12 times m-reduction [i] would yield (22, 24, large)-net in base 256, but