MinT - Best Known (251−115, 251, s)-Nets in Base 2

Best Known (251−115, 251, s)-Nets in Base 2

(251−115, 251, 66)-Net over F₂ — Constructive and digital

Digital (136, 251, 66)-net over F₂, using

1 times m-reduction [i] based on digital (136, 252, 66)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 97, 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 (39, 155, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(251−115, 251, 82)-Net over F₂ — Digital

Digital (136, 251, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−115, 251, 383)-Net in Base 2 — Upper bound on s

There is no (136, 251, 384)-net in base 2, because

1 times m-reduction [i] would yield (136, 250, 384)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2011 648414 095816 050943 112621 594183 345452 202937 924121 062525 154666 309156 353973 > 2²⁵⁰ [i]