Best Known (50−14, 50, s)-Nets in Base 49
(50−14, 50, 16907)-Net over F49 — Constructive and digital
Digital (36, 50, 16907)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 100)-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 (0, 7, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 3, 50)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (26, 40, 16807)-net over F49, using
- net defined by OOA [i] based on linear OOA(4940, 16807, F49, 14, 14) (dual of [(16807, 14), 235258, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- OA 7-folding and stacking [i] based on linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using
- net defined by OOA [i] based on linear OOA(4940, 16807, F49, 14, 14) (dual of [(16807, 14), 235258, 15]-NRT-code), using
- digital (3, 10, 100)-net over F49, using
(50−14, 50, 374047)-Net over F49 — Digital
Digital (36, 50, 374047)-net over F49, using
(50−14, 50, large)-Net in Base 49 — Upper bound on s
There is no (36, 50, large)-net in base 49, because
- 12 times m-reduction [i] would yield (36, 38, large)-net in base 49, but