Best Known (118−63, 118, s)-Nets in Base 9
(118−63, 118, 110)-Net over F9 — Constructive and digital
Digital (55, 118, 110)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 38, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-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 (7, 38, 36)-net over F9, using
(118−63, 118, 182)-Net over F9 — Digital
Digital (55, 118, 182)-net over F9, using
- t-expansion [i] based on digital (50, 118, 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
(118−63, 118, 6181)-Net in Base 9 — Upper bound on s
There is no (55, 118, 6182)-net in base 9, because
- 1 times m-reduction [i] would yield (55, 117, 6182)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 4433 770910 981326 392379 074823 815200 528472 422491 283024 136381 168701 099732 738706 088273 847583 852260 537222 768621 982225 > 9117 [i]