Best Known (29, 29+18, s)-Nets in Base 256
(29, 29+18, 7542)-Net over F256 — Constructive and digital
Digital (29, 47, 7542)-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 (17, 35, 7282)-net over F256, using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- digital (3, 12, 260)-net over F256, using
(29, 29+18, 128088)-Net over F256 — Digital
Digital (29, 47, 128088)-net over F256, using
(29, 29+18, large)-Net in Base 256 — Upper bound on s
There is no (29, 47, large)-net in base 256, because
- 16 times m-reduction [i] would yield (29, 31, large)-net in base 256, but