Best Known (28, 66, s)-Nets in Base 27
(28, 66, 132)-Net over F27 — Constructive and digital
Digital (28, 66, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 23, 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, 43, 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, 23, 64)-net over F27, using
(28, 66, 172)-Net in Base 27 — Constructive
(28, 66, 172)-net in base 27, using
- 18 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 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, 63, 172)-net over F81, using
(28, 66, 208)-Net over F27 — Digital
Digital (28, 66, 208)-net over F27, using
- t-expansion [i] based on digital (24, 66, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(28, 66, 244)-Net in Base 27
(28, 66, 244)-net in base 27, using
- 10 times m-reduction [i] based on (28, 76, 244)-net in base 27, using
- base change [i] based on digital (9, 57, 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, 57, 244)-net over F81, using
(28, 66, 28589)-Net in Base 27 — Upper bound on s
There is no (28, 66, 28590)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 29530 834614 113653 986893 219459 837916 746805 211597 928925 478080 599273 967003 592980 662977 745622 272113 > 2766 [i]