Best Known (9, 9+8, s)-Nets in Base 9
(9, 9+8, 164)-Net over F9 — Constructive and digital
Digital (9, 17, 164)-net over F9, using
- 1 times m-reduction [i] based on digital (9, 18, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 9, 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, 9, 82)-net over F81, using
(9, 9+8, 3142)-Net in Base 9 — Upper bound on s
There is no (9, 17, 3143)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 16696 715511 415521 > 917 [i]