Best Known (45−39, 45, s)-Nets in Base 27
(45−39, 45, 76)-Net over F27 — Constructive and digital
Digital (6, 45, 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
(45−39, 45, 619)-Net in Base 27 — Upper bound on s
There is no (6, 45, 620)-net in base 27, because
- 1 times m-reduction [i] would yield (6, 44, 620)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 961 367509 103813 732771 773503 950634 339324 728917 500200 084875 741553 > 2744 [i]