Best Known (74−47, 74, s)-Nets in Base 3
(74−47, 74, 37)-Net over F3 — Constructive and digital
Digital (27, 74, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
(74−47, 74, 39)-Net over F3 — Digital
Digital (27, 74, 39)-net over F3, using
- net from sequence [i] based on digital (27, 38)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 27 and N(F) ≥ 39, using
(74−47, 74, 101)-Net in Base 3 — Upper bound on s
There is no (27, 74, 102)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(374, 102, S3, 47), but
- the linear programming bound shows that M ≥ 24 172059 374503 335333 710062 818989 807752 718779 974987 / 100 882765 286875 > 374 [i]