Best Known (9, 19, s)-Nets in Base 9
(9, 19, 82)-Net over F9 — Constructive and digital
Digital (9, 19, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(9,81) in PG(18,9)) for nets [i] based on digital (0, 10, 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
(9, 19, 1374)-Net in Base 9 — Upper bound on s
There is no (9, 19, 1375)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 354942 964357 226201 > 919 [i]