Best Known (115−112, 115, s)-Nets in Base 3
(115−112, 115, 10)-Net over F3 — Constructive and digital
Digital (3, 115, 10)-net over F3, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
(115−112, 115, 11)-Net in Base 3 — Upper bound on s
There is no (3, 115, 12)-net in base 3, because
- 93 times m-reduction [i] would yield (3, 22, 12)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(322, 12, S3, 3, 19), but
- the linear programming bound for OOAs shows that M ≥ 28 839193 780671 / 895 > 322 [i]
- extracting embedded OOA [i] would yield OOA(322, 12, S3, 3, 19), but