Best Known (26−17, 26, s)-Nets in Base 49
(26−17, 26, 101)-Net over F49 — Constructive and digital
Digital (9, 26, 101)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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, 18, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 8, 50)-net over F49, using
(26−17, 26, 114)-Net over F49 — Digital
Digital (9, 26, 114)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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, 18, 64)-net over F49, using
- net from sequence [i] based on digital (1, 63)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
- net from sequence [i] based on digital (1, 63)-sequence over F49, using
- digital (0, 8, 50)-net over F49, using
(26−17, 26, 15003)-Net in Base 49 — Upper bound on s
There is no (9, 26, 15004)-net in base 49, because
- 1 times m-reduction [i] would yield (9, 25, 15004)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 1 798517 742666 711345 549369 831288 589401 887233 > 4925 [i]