Best Known (5, 5+12, s)-Nets in Base 3
(5, 5+12, 13)-Net over F3 — Constructive and digital
Digital (5, 17, 13)-net over F3, using
- net from sequence [i] based on digital (5, 12)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 4, N(F) = 12, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using an explicitly constructive algebraic function field [i]
(5, 5+12, 20)-Net over F3 — Upper bound on s (digital)
There is no digital (5, 17, 21)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
(5, 5+12, 27)-Net in Base 3 — Upper bound on s
There is no (5, 17, 28)-net in base 3, because
- extracting embedded OOA [i] would yield OOA(317, 28, S3, 2, 12), but
- the linear programming bound for OOAs shows that M ≥ 10966 234509 439272 414568 040575 840528 998238 357430 793969 / 76 011015 919608 959700 206806 326445 649459 962988 > 317 [i]