Best Known (31, 31+36, s)-Nets in Base 27
(31, 31+36, 158)-Net over F27 — Constructive and digital
Digital (31, 67, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 24, 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, 43, 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 (6, 24, 76)-net over F27, using
(31, 31+36, 224)-Net in Base 27 — Constructive
(31, 67, 224)-net in base 27, using
- 5 times m-reduction [i] based on (31, 72, 224)-net in base 27, using
- base change [i] based on digital (13, 54, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 54, 224)-net over F81, using
(31, 31+36, 299)-Net over F27 — Digital
Digital (31, 67, 299)-net over F27, using
(31, 31+36, 61793)-Net in Base 27 — Upper bound on s
There is no (31, 67, 61794)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 796848 116847 756308 397229 713019 882854 822184 278728 727536 769199 958973 763776 180069 055305 174074 945589 > 2767 [i]