Best Known (56, 56+63, s)-Nets in Base 9
(56, 56+63, 114)-Net over F9 — Constructive and digital
Digital (56, 119, 114)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 39, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (17, 80, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (8, 39, 40)-net over F9, using
(56, 56+63, 182)-Net over F9 — Digital
Digital (56, 119, 182)-net over F9, using
- t-expansion [i] based on digital (50, 119, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(56, 56+63, 6637)-Net in Base 9 — Upper bound on s
There is no (56, 119, 6638)-net in base 9, because
- 1 times m-reduction [i] would yield (56, 118, 6638)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 40005 371505 398184 390224 473870 078711 060400 128182 936237 827450 350853 088548 810015 220649 600957 321895 984734 030325 774545 > 9118 [i]