Best Known (9, 20, s)-Nets in Base 9
(9, 20, 44)-Net over F9 — Constructive and digital
Digital (9, 20, 44)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (3, 14, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (1, 6, 16)-net over F9, using
(9, 20, 48)-Net in Base 9 — Constructive
(9, 20, 48)-net in base 9, using
- 1 times m-reduction [i] based on (9, 21, 48)-net in base 9, using
- base change [i] based on digital (2, 14, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- base change [i] based on digital (2, 14, 48)-net over F27, using
(9, 20, 50)-Net over F9 — Digital
Digital (9, 20, 50)-net over F9, using
(9, 20, 1374)-Net in Base 9 — Upper bound on s
There is no (9, 20, 1375)-net in base 9, because
- 1 times m-reduction [i] would yield (9, 19, 1375)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 354942 964357 226201 > 919 [i]