MinT - Best Known (251−114, 251, s)-Nets in Base 2

Best Known (251−114, 251, s)-Nets in Base 2

(251−114, 251, 66)-Net over F₂ — Constructive and digital

Digital (137, 251, 66)-net over F₂, using

4 times m-reduction [i] based on digital (137, 255, 66)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 98, 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, 157, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(251−114, 251, 84)-Net over F₂ — Digital

Digital (137, 251, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−114, 251, 388)-Net in Base 2 — Upper bound on s

There is no (137, 251, 389)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3742 224133 815829 846792 483511 286875 487037 487646 568738 155419 624756 984340 787424 > 2²⁵¹ [i]