MinT - Best Known (4, 61, s)-Nets in Base 16

Best Known (4, 61, s)-Nets in Base 16

(4, 61, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 61, 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, 61, 142)-Net in Base 16 — Upper bound on s

There is no (4, 61, 143)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁶¹, 143, S₁₆, 57), but
- the linear programming bound shows that MÂ â‰¥ 3678 096040 664291 680628 131461 712861 579638 585564 090840 450961 366029 286830 610908 134759 727789 400821 917745 676288 / 125 076192 083828 905913 736083 497183 > 16⁶¹ [i]