Best Known (24−13, 24, s)-Nets in Base 9
(24−13, 24, 48)-Net over F9 — Constructive and digital
Digital (11, 24, 48)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (3, 16, 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 (2, 8, 20)-net over F9, using
(24−13, 24, 52)-Net in Base 9 — Constructive
(11, 24, 52)-net in base 9, using
- base change [i] based on digital (3, 16, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
(24−13, 24, 56)-Net over F9 — Digital
Digital (11, 24, 56)-net over F9, using
(24−13, 24, 1699)-Net in Base 9 — Upper bound on s
There is no (11, 24, 1700)-net in base 9, because
- 1 times m-reduction [i] would yield (11, 23, 1700)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 8889 444206 340073 005121 > 923 [i]