MinT - Best Known (4, 4+44, s)-Nets in Base 16

Best Known (4, 4+44, s)-Nets in Base 16

(4, 4+44, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 48, 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+44, 190)-Net in Base 16 — Upper bound on s

There is no (4, 48, 191)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴⁸, 191, S₁₆, 44), but
- the linear programming bound shows that MÂ â‰¥ 18 657005 053506 537283 163178 658138 899525 671358 562177 274988 748918 529945 143608 355514 744832 / 2898 107829 685518 680096 060297 > 16⁴⁸ [i]