Best Known (142−80, 142, s)-Nets in Base 9
(142−80, 142, 106)-Net over F9 — Constructive and digital
Digital (62, 142, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 45, 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, 97, 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, 45, 32)-net over F9, using
(142−80, 142, 192)-Net over F9 — Digital
Digital (62, 142, 192)-net over F9, using
- t-expansion [i] based on digital (61, 142, 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
(142−80, 142, 4786)-Net in Base 9 — Upper bound on s
There is no (62, 142, 4787)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 3184 505350 110679 876724 474345 709725 883316 689672 090182 821420 259974 594950 560438 168571 988563 169283 315009 176243 388715 793555 673110 676310 501825 > 9142 [i]