Best Known (100−55, 100, s)-Nets in Base 9
(100−55, 100, 96)-Net over F9 — Constructive and digital
Digital (45, 100, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 32, 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 (13, 68, 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 (5, 32, 32)-net over F9, using
(100−55, 100, 147)-Net over F9 — Digital
Digital (45, 100, 147)-net over F9, using
- t-expansion [i] based on digital (43, 100, 147)-net over F9, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 43 and N(F) ≥ 147, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
(100−55, 100, 4290)-Net in Base 9 — Upper bound on s
There is no (45, 100, 4291)-net in base 9, because
- 1 times m-reduction [i] would yield (45, 99, 4291)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 29521 540036 718874 352891 315316 122626 940382 849229 573959 306667 119820 505510 148805 078790 809550 843657 > 999 [i]