Best Known (3, 3+39, s)-Nets in Base 27
(3, 3+39, 52)-Net over F27 — Constructive and digital
Digital (3, 42, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
(3, 3+39, 56)-Net over F27 — Digital
Digital (3, 42, 56)-net over F27, using
- net from sequence [i] based on digital (3, 55)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 56, using
(3, 3+39, 332)-Net in Base 27 — Upper bound on s
There is no (3, 42, 333)-net in base 27, because
- 15 times m-reduction [i] would yield (3, 27, 333)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 457 888403 692103 449784 549605 743893 741649 > 2727 [i]