Best Known (57−44, 57, s)-Nets in Base 27
(57−44, 57, 96)-Net over F27 — Constructive and digital
Digital (13, 57, 96)-net over F27, using
- t-expansion [i] based on digital (11, 57, 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
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(57−44, 57, 136)-Net over F27 — Digital
Digital (13, 57, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(57−44, 57, 1768)-Net in Base 27 — Upper bound on s
There is no (13, 57, 1769)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3887 376562 712052 049609 450204 928687 783864 968885 977913 715008 320423 027132 567780 616473 > 2757 [i]