Best Known (25, 25+32, s)-Nets in Base 27
(25, 25+32, 132)-Net over F27 — Constructive and digital
Digital (25, 57, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 20, 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, 37, 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, 20, 64)-net over F27, using
(25, 25+32, 172)-Net in Base 27 — Constructive
(25, 57, 172)-net in base 27, using
- 15 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
(25, 25+32, 208)-Net over F27 — Digital
Digital (25, 57, 208)-net over F27, using
- t-expansion [i] based on digital (24, 57, 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
(25, 25+32, 244)-Net in Base 27
(25, 57, 244)-net in base 27, using
- 7 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
(25, 25+32, 32861)-Net in Base 27 — Upper bound on s
There is no (25, 57, 32862)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3870 557576 132640 814371 479026 019162 109577 801779 539470 207191 357300 898780 309763 485089 > 2757 [i]