MinT - Best Known (225−88, 225, s)-Nets in Base 2

Best Known (225−88, 225, s)-Nets in Base 2

(225−88, 225, 75)-Net over F₂ — Constructive and digital

Digital (137, 225, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 83, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 142, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(225−88, 225, 107)-Net over F₂ — Digital

Digital (137, 225, 107)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−88, 225, 535)-Net in Base 2 — Upper bound on s

There is no (137, 225, 536)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 57 961281 478554 300839 412585 662783 329246 403930 245771 168244 349995 218464 > 2²²⁵ [i]