Best Known (58, 134, s)-Nets in Base 9
(58, 134, 102)-Net over F9 — Constructive and digital
Digital (58, 134, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 41, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (17, 93, 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 (3, 41, 28)-net over F9, using
(58, 134, 182)-Net over F9 — Digital
Digital (58, 134, 182)-net over F9, using
- t-expansion [i] based on digital (50, 134, 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
(58, 134, 4328)-Net in Base 9 — Upper bound on s
There is no (58, 134, 4329)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 74 111653 967213 236723 254068 506901 973230 754129 054522 119699 500401 483838 007585 050762 561397 058437 622201 470536 574653 931086 899725 172081 > 9134 [i]