MinT - Best Known (4, 4+41, s)-Nets in Base 16

Best Known (4, 4+41, s)-Nets in Base 16

(4, 4+41, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 45, 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+41, 203)-Net in Base 16 — Upper bound on s

There is no (4, 45, 204)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴⁵, 204, S₁₆, 41), but
- the linear programming bound shows that MÂ â‰¥ 16 191997 313583 949083 930199 218519 124119 311901 684415 732998 818617 613493 372619 414655 194890 240000 / 10 527494 138365 391438 444858 450485 082927 > 16⁴⁵ [i]