MinT - Best Known (224−45, 224, s)-Nets in Base 2

Best Known (224−45, 224, s)-Nets in Base 2

(224−45, 224, 260)-Net over F₂ — Constructive and digital

Digital (179, 224, 260)-net over F₂, using

t-expansion [i] based on 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]

(224−45, 224, 562)-Net over F₂ — Digital

Digital (179, 224, 562)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−45, 224, 10158)-Net in Base 2 — Upper bound on s

There is no (179, 224, 10159)-net in base 2, because

1 times m-reduction [i] would yield (179, 223, 10159)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 502915 024981 372699 687214 254186 631177 054134 432329 634404 326374 453582 > 2²²³ [i]