Best Known (50−15, 50, s)-Nets in Base 49
(50−15, 50, 16857)-Net over F49 — Constructive and digital
Digital (35, 50, 16857)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (28, 43, 16807)-net over F49, using
- net defined by OOA [i] based on linear OOA(4943, 16807, F49, 15, 15) (dual of [(16807, 15), 252062, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using
- net defined by OOA [i] based on linear OOA(4943, 16807, F49, 15, 15) (dual of [(16807, 15), 252062, 16]-NRT-code), using
- digital (0, 7, 50)-net over F49, using
(50−15, 50, 136979)-Net over F49 — Digital
Digital (35, 50, 136979)-net over F49, using
(50−15, 50, large)-Net in Base 49 — Upper bound on s
There is no (35, 50, large)-net in base 49, because
- 13 times m-reduction [i] would yield (35, 37, large)-net in base 49, but