Best Known (12−8, 12, s)-Nets in Base 27
(12−8, 12, 64)-Net over F27 — Constructive and digital
Digital (4, 12, 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
(12−8, 12, 100)-Net in Base 27 — Constructive
(4, 12, 100)-net in base 27, using
- base change [i] based on digital (1, 9, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
(12−8, 12, 1673)-Net in Base 27 — Upper bound on s
There is no (4, 12, 1674)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 150113 187250 941097 > 2712 [i]