Best Known (5, 20, s)-Nets in Base 27
(5, 20, 68)-Net over F27 — Constructive and digital
Digital (5, 20, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
(5, 20, 72)-Net over F27 — Digital
Digital (5, 20, 72)-net over F27, using
- net from sequence [i] based on digital (5, 71)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 72, using
(5, 20, 82)-Net in Base 27 — Constructive
(5, 20, 82)-net in base 27, using
- base change [i] based on digital (0, 15, 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
(5, 20, 994)-Net in Base 27 — Upper bound on s
There is no (5, 20, 995)-net in base 27, because
- 1 times m-reduction [i] would yield (5, 19, 995)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1574 374477 328334 305292 690555 > 2719 [i]