MinT - Best Known (4, 4+39, s)-Nets in Base 16

Best Known (4, 4+39, s)-Nets in Base 16

(4, 4+39, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 43, 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+39, 210)-Net in Base 16 — Upper bound on s

There is no (4, 43, 211)-net in base 16, because

4 times m-reduction [i] would yield (4, 39, 211)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16³⁹, 211, S₁₆, 35), but
  - the linear programming bound shows that MÂ â‰¥ 81 063143 874310 794320 659731 456994 035370 740413 961466 015137 822814 674700 920789 401600 / 866 587492 621204 295082 820093 891499 > 16³⁹ [i]