Best Known (49−19, 49, s)-Nets in Base 256
(49−19, 49, 7541)-Net over F256 — Constructive and digital
Digital (30, 49, 7541)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 12, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (18, 37, 7281)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 7281, F256, 19, 19) (dual of [(7281, 19), 138302, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
- net defined by OOA [i] based on linear OOA(25637, 7281, F256, 19, 19) (dual of [(7281, 19), 138302, 20]-NRT-code), using
- digital (3, 12, 260)-net over F256, using
(49−19, 49, 106510)-Net over F256 — Digital
Digital (30, 49, 106510)-net over F256, using
(49−19, 49, large)-Net in Base 256 — Upper bound on s
There is no (30, 49, large)-net in base 256, because
- 17 times m-reduction [i] would yield (30, 32, large)-net in base 256, but