MinT - Best Known (4, 4+56, s)-Nets in Base 16

Best Known (4, 4+56, s)-Nets in Base 16

(4, 4+56, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 60, 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+56, 146)-Net in Base 16 — Upper bound on s

There is no (4, 60, 147)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁶⁰, 147, S₁₆, 56), but
- the linear programming bound shows that MÂ â‰¥ 939765 966922 797477 814596 181274 291363 410391 878783 132568 319700 182987 088048 908156 194099 962624 995855 466829 447168 / 521248 355323 503233 415469 012835 684063 > 16⁶⁰ [i]