Best Known (69−23, 69, s)-Nets in Base 3
(69−23, 69, 84)-Net over F3 — Constructive and digital
Digital (46, 69, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 23, 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
(69−23, 69, 137)-Net over F3 — Digital
Digital (46, 69, 137)-net over F3, using
(69−23, 69, 2174)-Net in Base 3 — Upper bound on s
There is no (46, 69, 2175)-net in base 3, because
- 1 times m-reduction [i] would yield (46, 68, 2175)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 278 732113 238564 254006 858615 480811 > 368 [i]