Best Known (51, 107, s)-Nets in Base 9
(51, 107, 108)-Net over F9 — Constructive and digital
Digital (51, 107, 108)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 34, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (17, 73, 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 (6, 34, 34)-net over F9, using
(51, 107, 182)-Net over F9 — Digital
Digital (51, 107, 182)-net over F9, using
- t-expansion [i] based on digital (50, 107, 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
(51, 107, 6241)-Net in Base 9 — Upper bound on s
There is no (51, 107, 6242)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 272010 974280 837656 067624 850844 833498 314588 083143 086879 012930 559560 912786 375374 555503 878700 033391 286593 > 9107 [i]