MinT - Best Known (211−40, 211, s)-Nets in Base 2

Best Known (211−40, 211, s)-Nets in Base 2

(211−40, 211, 270)-Net over F₂ — Constructive and digital

Digital (171, 211, 270)-net over F₂, using

2¹ times duplication [i] based on digital (170, 210, 270)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 26, 10)-net over F₂, using
    - net from sequence [i] based on digital (6, 9)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
    - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
  2. digital (144, 184, 260)-net over F₂, using
    - trace code for nets [i] based on digital (6, 46, 65)-net over F₁₆, using
      - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(211−40, 211, 645)-Net over F₂ — Digital

Digital (171, 211, 645)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−40, 211, 12420)-Net in Base 2 — Upper bound on s

There is no (171, 211, 12421)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3292 979615 884889 954711 887121 719671 205936 605966 624451 238719 266136 > 2²¹¹ [i]