Best Known (32, 79, s)-Nets in Base 27
(32, 79, 132)-Net over F27 — Constructive and digital
Digital (32, 79, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 27, 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, 52, 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, 27, 64)-net over F27, using
(32, 79, 172)-Net in Base 27 — Constructive
(32, 79, 172)-net in base 27, using
- 21 times m-reduction [i] based on (32, 100, 172)-net in base 27, using
- base change [i] based on digital (7, 75, 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, 75, 172)-net over F81, using
(32, 79, 208)-Net over F27 — Digital
Digital (32, 79, 208)-net over F27, using
- t-expansion [i] based on digital (24, 79, 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
(32, 79, 298)-Net in Base 27
(32, 79, 298)-net in base 27, using
- 1 times m-reduction [i] based on (32, 80, 298)-net in base 27, using
- base change [i] based on digital (12, 60, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 60, 298)-net over F81, using
(32, 79, 25910)-Net in Base 27 — Upper bound on s
There is no (32, 79, 25911)-net in base 27, because
- 1 times m-reduction [i] would yield (32, 78, 25911)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 4432 090438 127426 235494 298949 298274 366241 872011 759231 575959 030706 624146 673312 413303 515201 915243 293599 134937 635787 > 2778 [i]