Best Known (86−55, 86, s)-Nets in Base 3
(86−55, 86, 37)-Net over F3 — Constructive and digital
Digital (31, 86, 37)-net over F3, using
- t-expansion [i] based on digital (27, 86, 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]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(86−55, 86, 42)-Net over F3 — Digital
Digital (31, 86, 42)-net over F3, using
- t-expansion [i] based on digital (29, 86, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
(86−55, 86, 108)-Net in Base 3 — Upper bound on s
There is no (31, 86, 109)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(386, 109, S3, 55), but
- the linear programming bound shows that M ≥ 83016 139351 606949 579250 047731 105806 827665 847684 285103 / 601647 484900 > 386 [i]