Best Known (27−22, 27, s)-Nets in Base 3
(27−22, 27, 13)-Net over F3 — Constructive and digital
Digital (5, 27, 13)-net over F3, using
- net from sequence [i] based on digital (5, 12)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 4, N(F) = 12, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using an explicitly constructive algebraic function field [i]
(27−22, 27, 18)-Net in Base 3 — Upper bound on s
There is no (5, 27, 19)-net in base 3, because
- 5 times m-reduction [i] would yield (5, 22, 19)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(322, 19, S3, 2, 17), but
- the linear programming bound for OOAs shows that M ≥ 97 707447 325800 / 2867 > 322 [i]
- extracting embedded OOA [i] would yield OOA(322, 19, S3, 2, 17), but