Best Known (52, 52+71, s)-Nets in Base 9
(52, 52+71, 94)-Net over F9 — Constructive and digital
Digital (52, 123, 94)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (4, 39, 30)-net over F9, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- digital (13, 84, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (4, 39, 30)-net over F9, using
(52, 52+71, 96)-Net in Base 9 — Constructive
(52, 123, 96)-net in base 9, using
- base change [i] based on digital (11, 82, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(52, 52+71, 182)-Net over F9 — Digital
Digital (52, 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
(52, 52+71, 3663)-Net in Base 9 — Upper bound on s
There is no (52, 123, 3664)-net in base 9, because
- 1 times m-reduction [i] would yield (52, 122, 3664)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 263 405909 566723 481029 898946 997208 688913 965192 855694 835852 157662 375597 572723 356069 195351 542113 426492 815153 574039 479681 > 9122 [i]