MinT - Best Known (47−35, 47, s)-Nets in Base 4

Best Known (47−35, 47, s)-Nets in Base 4

(47−35, 47, 28)-Net over F₄ — Constructive and digital

Digital (12, 47, 28)-net over F₄, using

net from sequence [i] based on digital (12, 27)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]

(47−35, 47, 29)-Net over F₄ — Digital

Digital (12, 47, 29)-net over F₄, using

net from sequence [i] based on digital (12, 28)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 29, using
  - a curve from the manYPoints database [i]

(47−35, 47, 61)-Net in Base 4 — Upper bound on s

There is no (12, 47, 62)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁷, 62, S₄, 35), but
- the linear programming bound shows that MÂ â‰¥ 217 744891 226262 262890 190156 163220 242432 / 10152 833075 > 4⁴⁷ [i]