Best Known (138−80, 138, s)-Nets in Base 9
(138−80, 138, 96)-Net over F9 — Constructive and digital
Digital (58, 138, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 45, 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 (13, 93, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (5, 45, 32)-net over F9, using
(138−80, 138, 182)-Net over F9 — Digital
Digital (58, 138, 182)-net over F9, using
- t-expansion [i] based on digital (50, 138, 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
(138−80, 138, 3837)-Net in Base 9 — Upper bound on s
There is no (58, 138, 3838)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 485835 589092 417091 441932 515602 227362 206127 806254 989979 037641 808756 658779 830125 676191 418905 324229 783292 049647 237502 268819 555277 602945 > 9138 [i]