Best Known (52−30, 52, s)-Nets in Base 27
(52−30, 52, 116)-Net over F27 — Constructive and digital
Digital (22, 52, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 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
- digital (4, 34, 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 (3, 18, 52)-net over F27, using
(52−30, 52, 165)-Net over F27 — Digital
Digital (22, 52, 165)-net over F27, using
(52−30, 52, 172)-Net in Base 27 — Constructive
(22, 52, 172)-net in base 27, using
- 8 times m-reduction [i] based on (22, 60, 172)-net in base 27, using
- base change [i] based on digital (7, 45, 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, 45, 172)-net over F81, using
(52−30, 52, 244)-Net in Base 27
(22, 52, 244)-net in base 27, using
- base change [i] based on digital (9, 39, 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
(52−30, 52, 22631)-Net in Base 27 — Upper bound on s
There is no (22, 52, 22632)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 269 851624 767133 865576 735598 249539 462886 363374 544691 585059 731018 984233 821345 > 2752 [i]