Best Known (123−69, 123, s)-Nets in Base 9
(123−69, 123, 102)-Net over F9 — Constructive and digital
Digital (54, 123, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 37, 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, 86, 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, 37, 28)-net over F9, using
(123−69, 123, 182)-Net over F9 — Digital
Digital (54, 123, 182)-net over F9, using
- t-expansion [i] based on digital (50, 123, 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
(123−69, 123, 4471)-Net in Base 9 — Upper bound on s
There is no (54, 123, 4472)-net in base 9, because
- 1 times m-reduction [i] would yield (54, 122, 4472)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 263 159349 078940 601301 264285 793109 761398 467113 483788 203292 763561 148858 095644 572419 850399 252891 549506 532895 677967 963777 > 9122 [i]