Best Known (109−62, 109, s)-Nets in Base 7
(109−62, 109, 48)-Net over F7 — Constructive and digital
Digital (47, 109, 48)-net over F7, using
- net from sequence [i] based on digital (47, 47)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 47)-sequence over F49, using
- s-reduction 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]
- s-reduction based on digital (0, 49)-sequence over F49, using
- base reduction for sequences [i] based on digital (0, 47)-sequence over F49, using
(109−62, 109, 105)-Net over F7 — Digital
Digital (47, 109, 105)-net over F7, using
- t-expansion [i] based on digital (43, 109, 105)-net over F7, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
(109−62, 109, 1917)-Net in Base 7 — Upper bound on s
There is no (47, 109, 1918)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 130 715298 713770 999010 943736 051741 988830 709141 300123 954469 268723 471567 233101 078917 710963 788785 > 7109 [i]