MinT - Best Known (102−59, 102, s)-Nets in Base 16

Best Known (102−59, 102, s)-Nets in Base 16

(102−59, 102, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 102, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 102, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(102−59, 102, 226)-Net over F₁₆ — Digital

Digital (43, 102, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(102−59, 102, 12137)-Net in Base 16 — Upper bound on s

There is no (43, 102, 12138)-net in base 16, because

1 times m-reduction [i] would yield (43, 101, 12138)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 389568 028681 110539 120391 450621 008913 243062 234653 957976 237252 968908 092977 454828 854837 367834 775922 302145 182854 144718 757256 > 16¹⁰¹ [i]