Best Known (52, 113, s)-Nets in Base 9
(52, 113, 106)-Net over F9 — Constructive and digital
Digital (52, 113, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 35, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (17, 78, 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 (5, 35, 32)-net over F9, using
(52, 113, 182)-Net over F9 — Digital
Digital (52, 113, 182)-net over F9, using
- t-expansion [i] based on digital (50, 113, 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, 113, 5479)-Net in Base 9 — Upper bound on s
There is no (52, 113, 5480)-net in base 9, because
- 1 times m-reduction [i] would yield (52, 112, 5480)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 75115 847184 068803 491657 925162 783133 308298 742721 097718 992084 052485 846187 188479 686355 255481 222286 721985 822849 > 9112 [i]