MinT - Best Known (196, 196+47, s)-Nets in Base 2

Best Known (196, 196+47, s)-Nets in Base 2

(196, 196+47, 271)-Net over F₂ — Constructive and digital

Digital (196, 243, 271)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 31, 11)-net over F₂, using
  - net from sequence [i] based on digital (8, 10)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 8 and N(F) ≥ 11, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (165, 212, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 53, 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]

(196, 196+47, 677)-Net over F₂ — Digital

Digital (196, 243, 677)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(196, 196+47, 13827)-Net in Base 2 — Upper bound on s

There is no (196, 243, 13828)-net in base 2, because

1 times m-reduction [i] would yield (196, 242, 13828)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 070884 413718 358037 261755 912939 302782 918473 700735 985030 657775 564742 492288 > 2²⁴² [i]