Best Known (9−6, 9, s)-Nets in Base 7
(9−6, 9, 16)-Net over F7 — Constructive and digital
Digital (3, 9, 16)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using
- the rational function field F7(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- digital (0, 6, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7 (see above)
- digital (0, 3, 8)-net over F7, using
(9−6, 9, 20)-Net over F7 — Digital
Digital (3, 9, 20)-net over F7, using
- net from sequence [i] based on digital (3, 19)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 3 and N(F) ≥ 20, using
(9−6, 9, 102)-Net in Base 7 — Upper bound on s
There is no (3, 9, 103)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 41 071663 > 79 [i]