MinT - Best Known (47−30, 47, s)-Nets in Base 3

Best Known (47−30, 47, s)-Nets in Base 3

(47−30, 47, 28)-Net over F₃ — Constructive and digital

Digital (17, 47, 28)-net over F₃, using

t-expansion [i] based on digital (15, 47, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(47−30, 47, 77)-Net in Base 3 — Upper bound on s

There is no (17, 47, 78)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴⁷, 78, S₃, 30), but
- the linear programming bound shows that MÂ â‰¥ 376821 104619 807236 812558 836736 874455 567560 434974 259068 526097 / 14 022271 040758 320399 236352 203577 774400 > 3⁴⁷ [i]