Best Known (53, 119, s)-Nets in Base 9
(53, 119, 102)-Net over F9 — Constructive and digital
Digital (53, 119, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 36, 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, 83, 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, 36, 28)-net over F9, using
(53, 119, 182)-Net over F9 — Digital
Digital (53, 119, 182)-net over F9, using
- t-expansion [i] based on digital (50, 119, 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
(53, 119, 4522)-Net in Base 9 — Upper bound on s
There is no (53, 119, 4523)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 359671 179410 766857 134445 849079 102875 369217 665236 508794 544152 401850 601585 673205 994915 593778 853158 410943 025461 149785 > 9119 [i]