Best Known (55−30, 55, s)-Nets in Base 27
(55−30, 55, 140)-Net over F27 — Constructive and digital
Digital (25, 55, 140)-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 (6, 36, 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, 19, 64)-net over F27, using
(55−30, 55, 172)-Net in Base 27 — Constructive
(25, 55, 172)-net in base 27, using
- 17 times m-reduction [i] based on (25, 72, 172)-net in base 27, using
- base change [i] based on digital (7, 54, 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, 54, 172)-net over F81, using
(55−30, 55, 239)-Net over F27 — Digital
Digital (25, 55, 239)-net over F27, using
(55−30, 55, 244)-Net in Base 27
(25, 55, 244)-net in base 27, using
- 9 times m-reduction [i] based on (25, 64, 244)-net in base 27, using
- base change [i] based on digital (9, 48, 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, 48, 244)-net over F81, using
(55−30, 55, 43757)-Net in Base 27 — Upper bound on s
There is no (25, 55, 43758)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 5 309949 966019 252930 284494 581136 763113 949958 118294 613366 774892 056994 780328 143865 > 2755 [i]