Best Known (56−22, 56, s)-Nets in Base 256
(56−22, 56, 6217)-Net over F256 — Constructive and digital
Digital (34, 56, 6217)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (21, 43, 5958)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 5958, F256, 22, 22) (dual of [(5958, 22), 131033, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- OA 11-folding and stacking [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- net defined by OOA [i] based on linear OOA(25643, 5958, F256, 22, 22) (dual of [(5958, 22), 131033, 23]-NRT-code), using
- digital (2, 13, 259)-net over F256, using
(56−22, 56, 89945)-Net over F256 — Digital
Digital (34, 56, 89945)-net over F256, using
(56−22, 56, large)-Net in Base 256 — Upper bound on s
There is no (34, 56, large)-net in base 256, because
- 20 times m-reduction [i] would yield (34, 36, large)-net in base 256, but