MinT - Best Known (111−32, 111, s)-Nets in Base 2

Best Known (111−32, 111, s)-Nets in Base 2

(111−32, 111, 84)-Net over F₂ — Constructive and digital

Digital (79, 111, 84)-net over F₂, using

trace code for nets [i] based on digital (5, 37, 28)-net over F₈, using
- net from sequence [i] based on digital (5, 27)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]

(111−32, 111, 123)-Net over F₂ — Digital

Digital (79, 111, 123)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−32, 111, 810)-Net in Base 2 — Upper bound on s

There is no (79, 111, 811)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2628 687289 062967 195326 483107 423986 > 2¹¹¹ [i]