Best Known (52, 52+67, s)-Nets in Base 9
(52, 52+67, 98)-Net over F9 — Constructive and digital
Digital (52, 119, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 39, 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 (13, 80, 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 (6, 39, 34)-net over F9, using
(52, 52+67, 182)-Net over F9 — Digital
Digital (52, 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
(52, 52+67, 4230)-Net in Base 9 — Upper bound on s
There is no (52, 119, 4231)-net in base 9, because
- 1 times m-reduction [i] would yield (52, 118, 4231)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 40162 164193 211748 627996 097856 840715 308087 658775 605670 769051 219963 890903 691151 219385 872755 312112 927360 008247 442233 > 9118 [i]