Best Known (27, 27+45, s)-Nets in Base 3
(27, 27+45, 37)-Net over F3 — Constructive and digital
Digital (27, 72, 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+45, 39)-Net over F3 — Digital
Digital (27, 72, 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+45, 109)-Net in Base 3 — Upper bound on s
There is no (27, 72, 110)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(372, 110, S3, 45), but
- the linear programming bound shows that M ≥ 64 998937 666603 510979 018914 096721 964570 585523 728699 690213 148443 / 2635 072862 103122 792036 068099 > 372 [i]