Best Known (24, 24+30, s)-Nets in Base 27
(24, 24+30, 132)-Net over F27 — Constructive and digital
Digital (24, 54, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 19, 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, 35, 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, 19, 64)-net over F27, using
(24, 24+30, 172)-Net in Base 27 — Constructive
(24, 54, 172)-net in base 27, using
- 14 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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, 51, 172)-net over F81, using
(24, 24+30, 211)-Net over F27 — Digital
Digital (24, 54, 211)-net over F27, using
(24, 24+30, 244)-Net in Base 27
(24, 54, 244)-net in base 27, using
- 6 times m-reduction [i] based on (24, 60, 244)-net in base 27, using
- base change [i] based on digital (9, 45, 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, 45, 244)-net over F81, using
(24, 24+30, 35124)-Net in Base 27 — Upper bound on s
There is no (24, 54, 35125)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 196675 663703 790841 469074 557921 698680 236391 033001 372277 624848 727493 720078 838851 > 2754 [i]