Best Known (18, 18+19, s)-Nets in Base 9
(18, 18+19, 82)-Net over F9 — Constructive and digital
Digital (18, 37, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(18,81) in PG(36,9)) for nets [i] based on digital (0, 19, 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
(18, 18+19, 87)-Net over F9 — Digital
Digital (18, 37, 87)-net over F9, using
(18, 18+19, 3396)-Net in Base 9 — Upper bound on s
There is no (18, 37, 3397)-net in base 9, because
- 1 times m-reduction [i] would yield (18, 36, 3397)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 22583 768483 988785 292758 627361 708649 > 936 [i]