Best Known (40, 40+20, s)-Nets in Base 3
(40, 40+20, 84)-Net over F3 — Constructive and digital
Digital (40, 60, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 20, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
(40, 40+20, 125)-Net over F3 — Digital
Digital (40, 60, 125)-net over F3, using
(40, 40+20, 1641)-Net in Base 3 — Upper bound on s
There is no (40, 60, 1642)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 42585 580027 803637 867137 150357 > 360 [i]