MinT - Best Known (209−42, 209, s)-Nets in Base 2

Best Known (209−42, 209, s)-Nets in Base 2

(209−42, 209, 260)-Net over F₂ — Constructive and digital

Digital (167, 209, 260)-net over F₂, using

t-expansion [i] based on 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]

(209−42, 209, 531)-Net over F₂ — Digital

Digital (167, 209, 531)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−42, 209, 8568)-Net in Base 2 — Upper bound on s

There is no (167, 209, 8569)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 824 270251 475327 031499 364779 121414 631476 686831 717153 797489 897220 > 2²⁰⁹ [i]