Best Known (63, 63+86, s)-Nets in Base 9
(63, 63+86, 102)-Net over F9 — Constructive and digital
Digital (63, 149, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 46, 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, 103, 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, 46, 28)-net over F9, using
(63, 63+86, 192)-Net over F9 — Digital
Digital (63, 149, 192)-net over F9, using
- t-expansion [i] based on digital (61, 149, 192)-net over F9, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
(63, 63+86, 4248)-Net in Base 9 — Upper bound on s
There is no (63, 149, 4249)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 15254 783782 236816 760505 417849 866695 507567 649174 463035 672873 688683 565146 053559 557740 250812 650169 234334 488289 403247 084642 104233 355880 933987 596377 > 9149 [i]