MinT - Best Known (160, 160+37, s)-Nets in Base 2

Best Known (160, 160+37, s)-Nets in Base 2

(160, 160+37, 270)-Net over F₂ — Constructive and digital

Digital (160, 197, 270)-net over F₂, using

2¹ times duplication [i] based on digital (159, 196, 270)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 24, 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 (135, 172, 260)-net over F₂, using
    - trace code for nets [i] based on digital (6, 43, 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]

(160, 160+37, 630)-Net over F₂ — Digital

Digital (160, 197, 630)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+37, 14295)-Net in Base 2 — Upper bound on s

There is no (160, 197, 14296)-net in base 2, because

1 times m-reduction [i] would yield (160, 196, 14296)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 100458 288605 620367 998144 414930 587729 261979 763608 642245 590213 > 2¹⁹⁶ [i]