Best Known (32, 32+19, s)-Nets in Base 49
(32, 32+19, 500)-Net over F49 — Constructive and digital
Digital (32, 51, 500)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 50)-net over F49, using
- s-reduction based on digital (0, 1, s)-net over F49 with arbitrarily large s, using
- digital (0, 2, 50)-net over F49, using
- digital (0, 2, 50)-net over F49 (see above)
- digital (0, 2, 50)-net over F49 (see above)
- 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, 3, 50)-net over F49 (see above)
- digital (0, 4, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 9, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 19, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 1, 50)-net over F49, using
(32, 32+19, 9687)-Net over F49 — Digital
Digital (32, 51, 9687)-net over F49, using
(32, 32+19, large)-Net in Base 49 — Upper bound on s
There is no (32, 51, large)-net in base 49, because
- 17 times m-reduction [i] would yield (32, 34, large)-net in base 49, but