MinT - Best Known (4, 4+31, s)-Nets in Base 16

Best Known (4, 4+31, s)-Nets in Base 16

(4, 4+31, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 35, 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+31, 215)-Net in Base 16 — Upper bound on s

There is no (4, 35, 216)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16³⁵, 216, S₁₆, 31), but
- the linear programming bound shows that MÂ â‰¥ 8 230585 892540 415140 848140 944465 285737 503568 984674 737330 248159 854592 / 5 826071 715377 349518 504545 > 16³⁵ [i]