Best Known (67−55, 67, s)-Nets in Base 3
(67−55, 67, 20)-Net over F3 — Constructive and digital
Digital (12, 67, 20)-net over F3, using
- t-expansion [i] based on digital (11, 67, 20)-net over F3, using
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 9, N(F) = 19, and 1 place with degree 3 [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
(67−55, 67, 22)-Net over F3 — Digital
Digital (12, 67, 22)-net over F3, using
- net from sequence [i] based on digital (12, 21)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 12 and N(F) ≥ 22, using
(67−55, 67, 35)-Net in Base 3 — Upper bound on s
There is no (12, 67, 36)-net in base 3, because
- extracting embedded OOA [i] would yield OOA(367, 36, S3, 2, 55), but
- the LP bound with quadratic polynomials shows that M ≥ 5284 439399 430176 713888 429748 403459 / 56 > 367 [i]