Best Known (2, ∞, s)-Nets in Base 3
(2, ∞, 8)-Net over F3 — Constructive and digital
Digital (2, m, 8)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
(2, ∞, 9)-Net in Base 3 — Upper bound on s
There is no (2, m, 10)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (2, 13, 10)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(313, 10, S3, 3, 11), but
- the linear programming bound for OOAs shows that M ≥ 18 068994 / 11 > 313 [i]
- extracting embedded OOA [i] would yield OOA(313, 10, S3, 3, 11), but