MinT - Best Known (47−31, 47, s)-Nets in Base 3

Best Known (47−31, 47, s)-Nets in Base 3

(47−31, 47, 28)-Net over F₃ — Constructive and digital

Digital (16, 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]

(47−31, 47, 63)-Net in Base 3 — Upper bound on s

There is no (16, 47, 64)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴⁷, 64, S₃, 31), but
- the linear programming bound shows that MÂ â‰¥ 25 239311 848799 507508 016948 952760 / 828 304829 > 3⁴⁷ [i]