Best Known (1, 6, s)-Nets in Base 3
(1, 6, 7)-Net over F3 — Constructive and digital
Digital (1, 6, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
(1, 6, 8)-Net in Base 3 — Upper bound on s
There is no (1, 6, 9)-net in base 3, because
- 1 times m-reduction [i] would yield (1, 5, 9)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(35, 9, S3, 2, 4), but
- the linear programming bound for OOAs shows that M ≥ 981 / 4 > 35 [i]
- extracting embedded OOA [i] would yield OOA(35, 9, S3, 2, 4), but