Best Known (18−15, 18, s)-Nets in Base 9
(18−15, 18, 28)-Net over F9 — Constructive and digital
Digital (3, 18, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
(18−15, 18, 83)-Net in Base 9 — Upper bound on s
There is no (3, 18, 84)-net in base 9, because
- 1 times m-reduction [i] would yield (3, 17, 84)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 16762 225045 156065 > 917 [i]