Best Known (27, 27+49, s)-Nets in Base 3
(27, 27+49, 37)-Net over F3 — Constructive and digital
Digital (27, 76, 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]
(27, 27+49, 39)-Net over F3 — Digital
Digital (27, 76, 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
(27, 27+49, 96)-Net in Base 3 — Upper bound on s
There is no (27, 76, 97)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(376, 97, S3, 49), but
- the linear programming bound shows that M ≥ 66 667260 167200 192792 582029 034457 444120 479902 391671 / 35 100724 925000 > 376 [i]