Best Known (52−28, 52, s)-Nets in Base 27
(52−28, 52, 140)-Net over F27 — Constructive and digital
Digital (24, 52, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 18, 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 (6, 34, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 18, 64)-net over F27, using
(52−28, 52, 172)-Net in Base 27 — Constructive
(24, 52, 172)-net in base 27, using
- 16 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
(52−28, 52, 250)-Net over F27 — Digital
Digital (24, 52, 250)-net over F27, using
(52−28, 52, 48185)-Net in Base 27 — Upper bound on s
There is no (24, 52, 48186)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 269 773202 156766 360788 561092 285314 991980 338707 244633 773764 173433 218517 869213 > 2752 [i]