Best Known (45−24, 45, s)-Nets in Base 27
(45−24, 45, 132)-Net over F27 — Constructive and digital
Digital (21, 45, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 16, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (5, 29, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 16, 64)-net over F27, using
(45−24, 45, 172)-Net in Base 27 — Constructive
(21, 45, 172)-net in base 27, using
- 11 times m-reduction [i] based on (21, 56, 172)-net in base 27, using
- base change [i] based on digital (7, 42, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 42, 172)-net over F81, using
(45−24, 45, 241)-Net over F27 — Digital
Digital (21, 45, 241)-net over F27, using
(45−24, 45, 244)-Net in Base 27
(21, 45, 244)-net in base 27, using
- 3 times m-reduction [i] based on (21, 48, 244)-net in base 27, using
- base change [i] based on digital (9, 36, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 36, 244)-net over F81, using
(45−24, 45, 47418)-Net in Base 27 — Upper bound on s
There is no (21, 45, 47419)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 25788 556880 804951 122856 938940 730915 693710 826077 268225 341795 417001 > 2745 [i]