Best Known (27, 27+43, s)-Nets in Base 3
(27, 27+43, 37)-Net over F3 — Constructive and digital
Digital (27, 70, 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+43, 39)-Net over F3 — Digital
Digital (27, 70, 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+43, 122)-Net in Base 3 — Upper bound on s
There is no (27, 70, 123)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(370, 123, S3, 43), but
- the linear programming bound shows that M ≥ 40338 240718 208992 350334 953494 510547 694172 549255 456255 885012 220252 474180 796510 882011 301956 798022 532555 972566 923130 139936 591655 932172 328924 227210 945655 281618 925647 476596 995177 / 14 454896 235321 758861 324439 272066 920022 144150 020729 906272 529899 398511 133119 936981 919864 050312 440083 118680 206478 896586 841124 145201 887588 531250 > 370 [i]