MinT - Best Known (4, 31, s)-Nets in Base 16

Best Known (4, 31, s)-Nets in Base 16

(4, 31, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 31, 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, 31, 220)-Net in Base 16 — Upper bound on s

There is no (4, 31, 221)-net in base 16, because

1 times m-reduction [i] would yield (4, 30, 221)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 391241 215915 656824 299197 858296 344896 > 16³⁰ [i]