Best Known (47−13, 47, s)-Nets in Base 49
(47−13, 47, 19709)-Net over F49 — Constructive and digital
Digital (34, 47, 19709)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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 (1, 7, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 3, 50)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (24, 37, 19608)-net over F49, using
- net defined by OOA [i] based on linear OOA(4937, 19608, F49, 13, 13) (dual of [(19608, 13), 254867, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4937, 117649, F49, 13) (dual of [117649, 117612, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(4937, 117649, F49, 13) (dual of [117649, 117612, 14]-code), using
- net defined by OOA [i] based on linear OOA(4937, 19608, F49, 13, 13) (dual of [(19608, 13), 254867, 14]-NRT-code), using
- digital (4, 10, 101)-net over F49, using
(47−13, 47, 459262)-Net over F49 — Digital
Digital (34, 47, 459262)-net over F49, using
(47−13, 47, large)-Net in Base 49 — Upper bound on s
There is no (34, 47, large)-net in base 49, because
- 11 times m-reduction [i] would yield (34, 36, large)-net in base 49, but