MinT - Best Known (4, 59, s)-Nets in Base 16

Best Known (4, 59, s)-Nets in Base 16

(4, 59, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 59, 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, 59, 157)-Net in Base 16 — Upper bound on s

There is no (4, 59, 158)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁵⁹, 158, S₁₆, 55), but
- the linear programming bound shows that MÂ â‰¥ 1 751872 128079 872472 547941 838539 530895 802398 111785 402312 961189 355293 686055 441948 303058 733784 687094 938824 867840 / 15 835355 243697 262421 313219 417467 218513 > 16⁵⁹ [i]