Best Known (13−7, 13, s)-Nets in Base 9
(13−7, 13, 82)-Net over F9 — Constructive and digital
Digital (6, 13, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(6,81) in PG(12,9)) for nets [i] based on digital (0, 7, 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
(13−7, 13, 1488)-Net in Base 9 — Upper bound on s
There is no (6, 13, 1489)-net in base 9, because
- 1 times m-reduction [i] would yield (6, 12, 1489)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 282491 209817 > 912 [i]