Best Known (33−16, 33, s)-Nets in Base 9
(33−16, 33, 164)-Net over F9 — Constructive and digital
Digital (17, 33, 164)-net over F9, using
- 1 times m-reduction [i] based on digital (17, 34, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 17, 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
- trace code for nets [i] based on digital (0, 17, 82)-net over F81, using
(33−16, 33, 4058)-Net in Base 9 — Upper bound on s
There is no (17, 33, 4059)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 30 931437 579153 615075 090772 110529 > 933 [i]