MinT - Best Known (165, 165+44, s)-Nets in Base 2

Best Known (165, 165+44, s)-Nets in Base 2

(165, 165+44, 260)-Net over F₂ — Constructive and digital

Digital (165, 209, 260)-net over F₂, using

3 times m-reduction [i] based on 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]

(165, 165+44, 462)-Net over F₂ — Digital

Digital (165, 209, 462)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+44, 6523)-Net in Base 2 — Upper bound on s

There is no (165, 209, 6524)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 823 971142 691647 827939 403927 791943 779970 310277 354451 663507 446534 > 2²⁰⁹ [i]