Best Known (25, 25+35, s)-Nets in Base 27
(25, 25+35, 128)-Net over F27 — Constructive and digital
Digital (25, 60, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 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 (4, 39, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 21, 64)-net over F27, using
(25, 25+35, 172)-Net in Base 27 — Constructive
(25, 60, 172)-net in base 27, using
- 12 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+35, 208)-Net over F27 — Digital
Digital (25, 60, 208)-net over F27, using
- t-expansion [i] based on digital (24, 60, 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+35, 244)-Net in Base 27
(25, 60, 244)-net in base 27, using
- 4 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+35, 25615)-Net in Base 27 — Upper bound on s
There is no (25, 60, 25616)-net in base 27, because
- 1 times m-reduction [i] would yield (25, 59, 25616)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2 822697 443083 578231 005402 054811 557129 714090 821285 683201 677971 761819 217147 326086 838177 > 2759 [i]