MinT - Best Known (4, 4+43, s)-Nets in Base 16

Best Known (4, 4+43, s)-Nets in Base 16

(4, 4+43, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 47, 45)-net over F₁₆, using

net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
  - a function field by GarcÃa and Quoos [i]

(4, 4+43, 193)-Net in Base 16 — Upper bound on s

There is no (4, 47, 194)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴⁷, 194, S₁₆, 43), but
- the linear programming bound shows that MÂ â‰¥ 74 447463 223202 202288 558109 076867 793269 685342 575982 608010 507290 644917 691758 973309 419520 / 185793 019495 866981 042543 644779 > 16⁴⁷ [i]