MinT - Best Known (4, 57, s)-Nets in Base 16

Best Known (4, 57, s)-Nets in Base 16

(4, 57, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 57, 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, 57, 161)-Net in Base 16 — Upper bound on s

There is no (4, 57, 162)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁵⁷, 162, S₁₆, 53), but
- the linear programming bound shows that MÂ â‰¥ 68 064421 429565 073444 218271 835894 641922 164860 485347 516307 210053 372020 760005 649821 389598 325485 862912 / 156271 290683 540696 273382 153697 > 16⁵⁷ [i]