MinT - Best Known (249−68, 249, s)-Nets in Base 2

Best Known (249−68, 249, s)-Nets in Base 2

(249−68, 249, 195)-Net over F₂ — Constructive and digital

Digital (181, 249, 195)-net over F₂, using

t-expansion [i] based on digital (180, 249, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 83, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(249−68, 249, 269)-Net over F₂ — Digital

Digital (181, 249, 269)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−68, 249, 2118)-Net in Base 2 — Upper bound on s

There is no (181, 249, 2119)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 917 153693 584592 403373 685602 800738 756671 167381 060406 731342 086829 606429 340690 > 2²⁴⁹ [i]