Best Known (25, 25+38, s)-Nets in Base 27
(25, 25+38, 114)-Net over F27 — Constructive and digital
Digital (25, 63, 114)-net over F27, using
- t-expansion [i] based on digital (23, 63, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(25, 25+38, 172)-Net in Base 27 — Constructive
(25, 63, 172)-net in base 27, using
- 9 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+38, 208)-Net over F27 — Digital
Digital (25, 63, 208)-net over F27, using
- t-expansion [i] based on digital (24, 63, 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+38, 244)-Net in Base 27
(25, 63, 244)-net in base 27, using
- 1 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+38, 16986)-Net in Base 27 — Upper bound on s
There is no (25, 63, 16987)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 500862 391203 007064 550163 102138 452507 423877 467089 066701 799069 449503 872125 103129 094177 579779 > 2763 [i]