MinT - Best Known (152−35, 152, s)-Nets in Base 2

Best Known (152−35, 152, s)-Nets in Base 2

(152−35, 152, 195)-Net over F₂ — Constructive and digital

Digital (117, 152, 195)-net over F₂, using

t-expansion [i] based on digital (116, 152, 195)-net over F₂, using
- 1 times m-reduction [i] based on digital (116, 153, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 51, 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]

(152−35, 152, 277)-Net over F₂ — Digital

Digital (117, 152, 277)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−35, 152, 3361)-Net in Base 2 — Upper bound on s

There is no (117, 152, 3362)-net in base 2, because

1 times m-reduction [i] would yield (117, 151, 3362)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2855 011185 598291 002709 231585 323586 844516 247234 > 2¹⁵¹ [i]