Best Known (42, 42+23, s)-Nets in Base 256
(42, 42+23, 6729)-Net over F256 — Constructive and digital
Digital (42, 65, 6729)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (9, 20, 772)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- digital (0, 5, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- digital (1, 12, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (0, 3, 257)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (22, 45, 5957)-net over F256, using
- net defined by OOA [i] based on linear OOA(25645, 5957, F256, 23, 23) (dual of [(5957, 23), 136966, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25645, 65528, F256, 23) (dual of [65528, 65483, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25645, 65528, F256, 23) (dual of [65528, 65483, 24]-code), using
- net defined by OOA [i] based on linear OOA(25645, 5957, F256, 23, 23) (dual of [(5957, 23), 136966, 24]-NRT-code), using
- digital (9, 20, 772)-net over F256, using
(42, 42+23, 462996)-Net over F256 — Digital
Digital (42, 65, 462996)-net over F256, using
(42, 42+23, large)-Net in Base 256 — Upper bound on s
There is no (42, 65, large)-net in base 256, because
- 21 times m-reduction [i] would yield (42, 44, large)-net in base 256, but