Best Known (41−21, 41, s)-Nets in Base 9
(41−21, 41, 82)-Net over F9 — Constructive and digital
Digital (20, 41, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(20,81) in PG(40,9)) for nets [i] based on digital (0, 21, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(41−21, 41, 93)-Net over F9 — Digital
Digital (20, 41, 93)-net over F9, using
(41−21, 41, 3708)-Net in Base 9 — Upper bound on s
There is no (20, 41, 3709)-net in base 9, because
- 1 times m-reduction [i] would yield (20, 40, 3709)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 148 057176 420973 031357 472997 913771 370705 > 940 [i]