Best Known (5−4, 5, s)-Nets in Base 9
(5−4, 5, 16)-Net over F9 — Constructive and digital
Digital (1, 5, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
(5−4, 5, 42)-Net in Base 9 — Upper bound on s
There is no (1, 5, 43)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 61233 > 95 [i]
- extracting embedded orthogonal array [i] would yield OA(95, 43, S9, 4), but
- the linear programming bound shows that M ≥ 4 035015 / 67 > 95 [i]