Best Known (54, 54+62, s)-Nets in Base 9
(54, 54+62, 108)-Net over F9 — Constructive and digital
Digital (54, 116, 108)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 37, 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, 79, 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, 37, 34)-net over F9, using
(54, 54+62, 182)-Net over F9 — Digital
Digital (54, 116, 182)-net over F9, using
- t-expansion [i] based on digital (50, 116, 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, 54+62, 5757)-Net in Base 9 — Upper bound on s
There is no (54, 116, 5758)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 493 409432 538188 564596 195758 041450 127746 076211 576941 951438 144833 722598 264779 373764 343991 360024 247967 343391 133265 > 9116 [i]