MinT - Best Known (4, 4+32, s)-Nets in Base 16

Best Known (4, 4+32, s)-Nets in Base 16

(4, 4+32, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 36, 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+32, 213)-Net in Base 16 — Upper bound on s

There is no (4, 36, 214)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16³⁶, 214, S₁₆, 32), but
- the linear programming bound shows that MÂ â‰¥ 5 349140 094645 134083 090591 612030 894633 013545 166620 968636 776542 962263 785472 / 231916 737981 753734 765621 508227 > 16³⁶ [i]