Best Known (27, 27+44, s)-Nets in Base 3
(27, 27+44, 37)-Net over F3 — Constructive and digital
Digital (27, 71, 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+44, 39)-Net over F3 — Digital
Digital (27, 71, 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+44, 115)-Net in Base 3 — Upper bound on s
There is no (27, 71, 116)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(371, 116, S3, 44), but
- the linear programming bound shows that M ≥ 14 025459 045181 162136 379342 052897 409149 404545 702710 558278 410116 209802 571675 970589 918360 470043 310367 / 1769 005051 949568 456588 851621 598563 470220 189319 817727 801453 117375 > 371 [i]