MinT - Best Known (239−98, 239, s)-Nets in Base 2

Best Known (239−98, 239, s)-Nets in Base 2

(239−98, 239, 70)-Net over F₂ — Constructive and digital

Digital (141, 239, 70)-net over F₂, using

2 times m-reduction [i] based on digital (141, 241, 70)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 71, 21)-net over F₂, using
    - net from sequence [i] based on digital (21, 20)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
  2. digital (70, 170, 49)-net over F₂, using
    - net from sequence [i] based on digital (70, 48)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, and 1 place with degree 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(239−98, 239, 101)-Net over F₂ — Digital

Digital (141, 239, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−98, 239, 492)-Net in Base 2 — Upper bound on s

There is no (141, 239, 493)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 893167 788839 133915 849029 942955 507807 607767 976166 792243 323752 425018 267848 > 2²³⁹ [i]