MinT - Best Known (116−25, 116, s)-Nets in Base 2

Best Known (116−25, 116, s)-Nets in Base 2

(116−25, 116, 180)-Net over F₂ — Constructive and digital

Digital (91, 116, 180)-net over F₂, using

trace code for nets [i] based on digital (4, 29, 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]

(116−25, 116, 274)-Net over F₂ — Digital

Digital (91, 116, 274)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−25, 116, 4039)-Net in Base 2 — Upper bound on s

There is no (91, 116, 4040)-net in base 2, because

1 times m-reduction [i] would yield (91, 115, 4040)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 41564 428037 039659 431690 633714 782088 > 2¹¹⁵ [i]