Best Known (40, 40+25, s)-Nets in Base 256
(40, 40+25, 5722)-Net over F256 — Constructive and digital
Digital (40, 65, 5722)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (4, 16, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (24, 49, 5461)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
- digital (4, 16, 261)-net over F256, using
(40, 40+25, 127991)-Net over F256 — Digital
Digital (40, 65, 127991)-net over F256, using
(40, 40+25, large)-Net in Base 256 — Upper bound on s
There is no (40, 65, large)-net in base 256, because
- 23 times m-reduction [i] would yield (40, 42, large)-net in base 256, but