MinT - Best Known (236−95, 236, s)-Nets in Base 2

Best Known (236−95, 236, s)-Nets in Base 2

(236−95, 236, 75)-Net over F₂ — Constructive and digital

Digital (141, 236, 75)-net over F₂, using

1 times m-reduction [i] based on digital (141, 237, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 87, 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, 150, 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]

(236−95, 236, 105)-Net over F₂ — Digital

Digital (141, 236, 105)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−95, 236, 521)-Net in Base 2 — Upper bound on s

There is no (141, 236, 522)-net in base 2, because

1 times m-reduction [i] would yield (141, 235, 522)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 57896 291757 503623 224439 060155 237936 140062 494583 637918 263157 462038 953216 > 2²³⁵ [i]