Best Known (75−48, 75, s)-Nets in Base 3
(75−48, 75, 37)-Net over F3 — Constructive and digital
Digital (27, 75, 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]
(75−48, 75, 39)-Net over F3 — Digital
Digital (27, 75, 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
(75−48, 75, 99)-Net in Base 3 — Upper bound on s
There is no (27, 75, 100)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(375, 100, S3, 48), but
- the linear programming bound shows that M ≥ 226 805771 897859 565583 876956 237485 928730 202904 705179 / 269 019371 489414 > 375 [i]