Best Known (30, 30+45, s)-Nets in Base 27
(30, 30+45, 128)-Net over F27 — Constructive and digital
Digital (30, 75, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 26, 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, 49, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 26, 64)-net over F27, using
(30, 30+45, 172)-Net in Base 27 — Constructive
(30, 75, 172)-net in base 27, using
- 17 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 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, 69, 172)-net over F81, using
(30, 30+45, 208)-Net over F27 — Digital
Digital (30, 75, 208)-net over F27, using
- t-expansion [i] based on digital (24, 75, 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
(30, 30+45, 244)-Net in Base 27
(30, 75, 244)-net in base 27, using
- 9 times m-reduction [i] based on (30, 84, 244)-net in base 27, using
- base change [i] based on digital (9, 63, 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, 63, 244)-net over F81, using
(30, 30+45, 22711)-Net in Base 27 — Upper bound on s
There is no (30, 75, 22712)-net in base 27, because
- 1 times m-reduction [i] would yield (30, 74, 22712)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 8337 517810 062554 096349 279069 141203 462724 170968 439158 003150 047138 658074 085861 977527 137067 055397 768019 863377 > 2774 [i]