Best Known (54, 118, s)-Nets in Base 9
(54, 118, 106)-Net over F9 — Constructive and digital
Digital (54, 118, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 37, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (17, 81, 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 (5, 37, 32)-net over F9, using
(54, 118, 182)-Net over F9 — Digital
Digital (54, 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
(54, 118, 5259)-Net in Base 9 — Upper bound on s
There is no (54, 118, 5260)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 39959 615763 713451 234617 848288 928486 303812 114410 220445 564842 198449 499795 361935 185527 551206 749725 401586 223521 190913 > 9118 [i]