MinT - Best Known (4, 34, s)-Nets in Base 16

Best Known (4, 34, s)-Nets in Base 16

(4, 34, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 34, 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, 34, 219)-Net in Base 16 — Upper bound on s

There is no (4, 34, 220)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16³⁴, 220, S₁₆, 30), but
- the linear programming bound shows that MÂ â‰¥ 43 722163 361541 064795 296934 453065 268768 645180 256952 780990 568090 027000 070144 / 498 692967 628197 125257 911465 059569 > 16³⁴ [i]