Best Known (73−31, 73, s)-Nets in Base 27
(73−31, 73, 222)-Net over F27 — Constructive and digital
Digital (42, 73, 222)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 14, 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 (6, 21, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 38, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 14, 64)-net over F27, using
(73−31, 73, 370)-Net in Base 27 — Constructive
(42, 73, 370)-net in base 27, using
- 31 times m-reduction [i] based on (42, 104, 370)-net in base 27, using
- base change [i] based on digital (16, 78, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 78, 370)-net over F81, using
(73−31, 73, 1424)-Net over F27 — Digital
Digital (42, 73, 1424)-net over F27, using
(73−31, 73, 1833739)-Net in Base 27 — Upper bound on s
There is no (42, 73, 1833740)-net in base 27, because
- 1 times m-reduction [i] would yield (42, 72, 1833740)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 11 433887 193778 841272 282786 302784 520274 961450 759466 041026 859678 252434 649850 613417 507176 981166 723051 645873 > 2772 [i]