Best Known (27, 27+46, s)-Nets in Base 3
(27, 27+46, 37)-Net over F3 — Constructive and digital
Digital (27, 73, 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+46, 39)-Net over F3 — Digital
Digital (27, 73, 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+46, 106)-Net in Base 3 — Upper bound on s
There is no (27, 73, 107)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(373, 107, S3, 46), but
- the linear programming bound shows that M ≥ 173 709034 524083 549814 758117 123043 291766 878451 928899 795839 / 2109 537706 365678 947800 > 373 [i]