Best Known (51−12, 51, s)-Nets in Base 49
(51−12, 51, 960850)-Net over F49 — Constructive and digital
Digital (39, 51, 960850)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (33, 45, 960800)-net over F49, using
- net defined by OOA [i] based on linear OOA(4945, 960800, F49, 12, 12) (dual of [(960800, 12), 11529555, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4945, 5764800, F49, 12) (dual of [5764800, 5764755, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(4945, 5764800, F49, 12) (dual of [5764800, 5764755, 13]-code), using
- net defined by OOA [i] based on linear OOA(4945, 960800, F49, 12, 12) (dual of [(960800, 12), 11529555, 13]-NRT-code), using
- digital (0, 6, 50)-net over F49, using
(51−12, 51, 7016765)-Net over F49 — Digital
Digital (39, 51, 7016765)-net over F49, using
(51−12, 51, large)-Net in Base 49 — Upper bound on s
There is no (39, 51, large)-net in base 49, because
- 10 times m-reduction [i] would yield (39, 41, large)-net in base 49, but