MinT - Best Known (251−53, 251, s)-Nets in Base 2

Best Known (251−53, 251, s)-Nets in Base 2

(251−53, 251, 260)-Net over F₂ — Constructive and digital

Digital (198, 251, 260)-net over F₂, using

5 times m-reduction [i] based on digital (198, 256, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 64, 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]

(251−53, 251, 534)-Net over F₂ — Digital

Digital (198, 251, 534)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−53, 251, 8237)-Net in Base 2 — Upper bound on s

There is no (198, 251, 8238)-net in base 2, because

1 times m-reduction [i] would yield (198, 250, 8238)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1812 525821 795411 138847 953835 964560 820921 096059 251920 100084 405040 720317 409484 > 2²⁵⁰ [i]