Best Known (47−23, 47, s)-Nets in Base 9
(47−23, 47, 164)-Net over F9 — Constructive and digital
Digital (24, 47, 164)-net over F9, using
- 1 times m-reduction [i] based on digital (24, 48, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 24, 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
- trace code for nets [i] based on digital (0, 24, 82)-net over F81, using
(47−23, 47, 5996)-Net in Base 9 — Upper bound on s
There is no (24, 47, 5997)-net in base 9, because
- 1 times m-reduction [i] would yield (24, 46, 5997)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 78 556594 366170 369662 182467 738903 334105 273017 > 946 [i]