Best Known (11, 11+31, s)-Nets in Base 27
(11, 11+31, 96)-Net over F27 — Constructive and digital
Digital (11, 42, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
(11, 11+31, 100)-Net over F27 — Digital
Digital (11, 42, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(11, 11+31, 2011)-Net in Base 27 — Upper bound on s
There is no (11, 42, 2012)-net in base 27, because
- 1 times m-reduction [i] would yield (11, 41, 2012)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 48639 041897 485159 868157 646331 559177 679101 235342 647551 010033 > 2741 [i]