Best Known (37, 37+20, s)-Nets in Base 256
(37, 37+20, 7324)-Net over F256 — Constructive and digital
Digital (37, 57, 7324)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (8, 18, 771)-net over F256, using
- 1 times m-reduction [i] based on digital (8, 19, 771)-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 (0, 11, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- digital (0, 3, 257)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- 1 times m-reduction [i] based on digital (8, 19, 771)-net over F256, using
- digital (19, 39, 6553)-net over F256, using
- net defined by OOA [i] based on linear OOA(25639, 6553, F256, 20, 20) (dual of [(6553, 20), 131021, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(25639, 65530, F256, 20) (dual of [65530, 65491, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(25639, 65530, F256, 20) (dual of [65530, 65491, 21]-code), using
- net defined by OOA [i] based on linear OOA(25639, 6553, F256, 20, 20) (dual of [(6553, 20), 131021, 21]-NRT-code), using
- digital (8, 18, 771)-net over F256, using
(37, 37+20, 521679)-Net over F256 — Digital
Digital (37, 57, 521679)-net over F256, using
(37, 37+20, large)-Net in Base 256 — Upper bound on s
There is no (37, 57, large)-net in base 256, because
- 18 times m-reduction [i] would yield (37, 39, large)-net in base 256, but