MinT - Best Known (107−22, 107, s)-Nets in Base 2

Best Known (107−22, 107, s)-Nets in Base 2

(107−22, 107, 180)-Net over F₂ — Constructive and digital

Digital (85, 107, 180)-net over F₂, using

1 times m-reduction [i] based on digital (85, 108, 180)-net over F₂, using
- trace code for nets [i] based on digital (4, 27, 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]

(107−22, 107, 303)-Net over F₂ — Digital

Digital (85, 107, 303)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−22, 107, 4145)-Net in Base 2 — Upper bound on s

There is no (85, 107, 4146)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 162 605588 009432 853910 035765 448032 > 2¹⁰⁷ [i]