MinT - Best Known (143, 239, s)-Nets in Base 2

Best Known (143, 239, s)-Nets in Base 2

(143, 239, 75)-Net over F₂ — Constructive and digital

Digital (143, 239, 75)-net over F₂, using

4 times m-reduction [i] based on digital (143, 243, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 89, 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, 154, 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]

(143, 239, 106)-Net over F₂ — Digital

Digital (143, 239, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 239, 523)-Net in Base 2 — Upper bound on s

There is no (143, 239, 524)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 933532 155278 533923 989192 893874 499441 340166 164319 170596 266109 081331 411296 > 2²³⁹ [i]