Best Known (28, 28+39, s)-Nets in Base 3
(28, 28+39, 37)-Net over F3 — Constructive and digital
Digital (28, 67, 37)-net over F3, using
- t-expansion [i] based on digital (27, 67, 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
(28, 28+39, 39)-Net over F3 — Digital
Digital (28, 67, 39)-net over F3, using
- t-expansion [i] based on digital (27, 67, 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
- net from sequence [i] based on digital (27, 38)-sequence over F3, using
(28, 28+39, 160)-Net in Base 3 — Upper bound on s
There is no (28, 67, 161)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(367, 161, S3, 39), but
- the linear programming bound shows that M ≥ 7869 930401 701596 807600 626345 198645 987250 178540 123516 450258 613760 580612 231642 212759 197575 489472 106615 287923 905883 555477 227637 750454 750095 263289 921478 546175 064686 283056 062869 623904 743004 569600 / 82 148594 495356 629216 229580 554269 756505 456638 376053 336365 080668 371924 625544 809288 130216 022035 376144 707077 418285 944925 300421 885924 252263 109749 469346 381267 111193 > 367 [i]