MinT - Best Known (15, 15+43, s)-Nets in Base 4

Best Known (15, 15+43, s)-Nets in Base 4

(15, 15+43, 33)-Net over F₄ — Constructive and digital

Digital (15, 58, 33)-net over F₄, using

net from sequence [i] based on digital (15, 32)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]

(15, 15+43, 35)-Net over F₄ — Digital

Digital (15, 58, 35)-net over F₄, using

net from sequence [i] based on digital (15, 34)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 35, using
  - a curve from the manYPoints database [i]

(15, 15+43, 72)-Net in Base 4 — Upper bound on s

There is no (15, 58, 73)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵⁸, 73, S₄, 43), but
- the linear programming bound shows that MÂ â‰¥ 2189 401164 029144 651258 105721 344079 901877 075968 / 23088 690625 > 4⁵⁸ [i]