Best Known (140−78, 140, s)-Nets in Base 9
(140−78, 140, 108)-Net over F9 — Constructive and digital
Digital (62, 140, 108)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 45, 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 (17, 95, 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 (6, 45, 34)-net over F9, using
(140−78, 140, 192)-Net over F9 — Digital
Digital (62, 140, 192)-net over F9, using
- t-expansion [i] based on digital (61, 140, 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
(140−78, 140, 5102)-Net in Base 9 — Upper bound on s
There is no (62, 140, 5103)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 39 361630 967728 549394 043053 259051 583040 170598 703095 052951 417478 543051 922332 854947 814703 005317 783090 475409 836381 427822 535191 924479 460681 > 9140 [i]