MinT - Best Known (40, 40+30, s)-Nets in Base 2

Best Known (40, 40+30, s)-Nets in Base 2

(40, 40+30, 34)-Net over F₂ — Constructive and digital

Digital (40, 70, 34)-net over F₂, using

trace code for nets [i] based on digital (5, 35, 17)-net over F₄, using
- net from sequence [i] based on digital (5, 16)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]

(40, 40+30, 35)-Net over F₂ — Digital

Digital (40, 70, 35)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+30, 142)-Net in Base 2 — Upper bound on s

There is no (40, 70, 143)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1248 160283 582693 534078 > 2⁷⁰ [i]