Best Known (4, 4+9, s)-Nets in Base 27
(4, 4+9, 64)-Net over F27 — Constructive and digital
Digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
(4, 4+9, 82)-Net in Base 27 — Constructive
(4, 13, 82)-net in base 27, using
- 3 times m-reduction [i] based on (4, 16, 82)-net in base 27, using
- base change [i] based on digital (0, 12, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- base change [i] based on digital (0, 12, 82)-net over F81, using
(4, 4+9, 1673)-Net in Base 27 — Upper bound on s
There is no (4, 13, 1674)-net in base 27, because
- 1 times m-reduction [i] would yield (4, 12, 1674)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 150113 187250 941097 > 2712 [i]