MinT - Best Known (44, 77, s)-Nets in Base 2

Best Known (44, 77, s)-Nets in Base 2

(44, 77, 34)-Net over F₂ — Constructive and digital

Digital (44, 77, 34)-net over F₂, using

1 times m-reduction [i] based on digital (44, 78, 34)-net over F₂, using
- trace code for nets [i] based on digital (5, 39, 17)-net over F₄, using
  - net from sequence [i] based on digital (5, 16)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
      - an explicitly constructive algebraic function field [i]

(44, 77, 38)-Net over F₂ — Digital

Digital (44, 77, 38)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 77, 160)-Net in Base 2 — Upper bound on s

There is no (44, 77, 161)-net in base 2, because

1 times m-reduction [i] would yield (44, 76, 161)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 77091 780144 978274 443006 > 2⁷⁶ [i]