MinT - Best Known (224−47, 224, s)-Nets in Base 2

Best Known (224−47, 224, s)-Nets in Base 2

(224−47, 224, 260)-Net over F₂ — Constructive and digital

Digital (177, 224, 260)-net over F₂, using

4 times m-reduction [i] based on digital (177, 228, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 57, 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]

(224−47, 224, 494)-Net over F₂ — Digital

Digital (177, 224, 494)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−47, 224, 7784)-Net in Base 2 — Upper bound on s

There is no (177, 224, 7785)-net in base 2, because

1 times m-reduction [i] would yield (177, 223, 7785)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 486443 171741 951495 107769 027664 276308 366678 892376 403932 328902 361088 > 2²²³ [i]