Best Known (18−12, 18, s)-Nets in Base 27
(18−12, 18, 76)-Net over F27 — Constructive and digital
Digital (6, 18, 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
(18−12, 18, 100)-Net in Base 27 — Constructive
(6, 18, 100)-net in base 27, using
- 2 times m-reduction [i] based on (6, 20, 100)-net in base 27, using
- base change [i] based on digital (1, 15, 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
- base change [i] based on digital (1, 15, 100)-net over F81, using
(18−12, 18, 2263)-Net in Base 27 — Upper bound on s
There is no (6, 18, 2264)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 58 197749 054363 129746 340625 > 2718 [i]