Best Known (1, 1+12, s)-Nets in Base 3
(1, 1+12, 7)-Net over F3 — Constructive and digital
Digital (1, 13, 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, 1+12, 7)-Net in Base 3 — Upper bound on s
There is no (1, 13, 8)-net in base 3, because
- 6 times m-reduction [i] would yield (1, 7, 8)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(37, 8, S3, 2, 6), but
- the linear programming bound for OOAs shows that M ≥ 111537 / 49 > 37 [i]
- extracting embedded OOA [i] would yield OOA(37, 8, S3, 2, 6), but