MinT - Best Known (112−24, 112, s)-Nets in Base 2

Best Known (112−24, 112, s)-Nets in Base 2

(112−24, 112, 180)-Net over F₂ — Constructive and digital

Digital (88, 112, 180)-net over F₂, using

trace code for nets [i] based on digital (4, 28, 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]

(112−24, 112, 273)-Net over F₂ — Digital

Digital (88, 112, 273)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−24, 112, 3394)-Net in Base 2 — Upper bound on s

There is no (88, 112, 3395)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5205 631090 111686 176260 048010 761904 > 2¹¹² [i]