MinT - Best Known (3, 3+36, s)-Nets in Base 16

Best Known (3, 3+36, s)-Nets in Base 16

(3, 3+36, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 39, 38)-net over F₁₆, using

net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
  - a function field by SÃ©mirat [i]

(3, 3+36, 161)-Net in Base 16 — Upper bound on s

There is no (3, 39, 162)-net in base 16, because

4 times m-reduction [i] would yield (3, 35, 162)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16³⁵, 162, S₁₆, 32), but
  - the linear programming bound shows that MÂ â‰¥ 4853 573546 032429 937192 168908 048884 147376 956821 677601 984190 873600 / 3413 823898 487425 614953 > 16³⁵ [i]