Best Known (78−51, 78, s)-Nets in Base 3
(78−51, 78, 37)-Net over F3 — Constructive and digital
Digital (27, 78, 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]
(78−51, 78, 39)-Net over F3 — Digital
Digital (27, 78, 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
(78−51, 78, 92)-Net in Base 3 — Upper bound on s
There is no (27, 78, 93)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(378, 93, S3, 51), but
- the linear programming bound shows that M ≥ 2117 985825 855951 548682 979121 686352 501183 391624 / 117 447583 > 378 [i]