MinT - Best Known (111−57, 111, s)-Nets in Base 16

Best Known (111−57, 111, s)-Nets in Base 16

(111−57, 111, 243)-Net over F₁₆ — Constructive and digital

Digital (54, 111, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 111, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(111−57, 111, 342)-Net over F₁₆ — Digital

Digital (54, 111, 342)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−57, 111, 40478)-Net in Base 16 — Upper bound on s

There is no (54, 111, 40479)-net in base 16, because

1 times m-reduction [i] would yield (54, 110, 40479)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 840946 774917 448245 380107 367668 478073 446946 602834 722263 226779 142974 266169 109908 864819 641172 027432 646435 327058 487212 904895 975892 422931 > 16¹¹⁰ [i]