MinT - Best Known (61, 61+25, s)-Nets in Base 2

Best Known (61, 61+25, s)-Nets in Base 2

(61, 61+25, 72)-Net over F₂ — Constructive and digital

Digital (61, 86, 72)-net over F₂, using

1 times m-reduction [i] based on digital (61, 87, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 29, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(61, 61+25, 101)-Net over F₂ — Digital

Digital (61, 86, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+25, 699)-Net in Base 2 — Upper bound on s

There is no (61, 86, 700)-net in base 2, because

1 times m-reduction [i] would yield (61, 85, 700)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 38 738874 080772 811369 173676 > 2⁸⁵ [i]