MinT - Best Known (57−25, 57, s)-Nets in Base 2

Best Known (57−25, 57, s)-Nets in Base 2

(57−25, 57, 28)-Net over F₂ — Constructive and digital

Digital (32, 57, 28)-net over F₂, using

1 times m-reduction [i] based on digital (32, 58, 28)-net over F₂, using
- trace code for nets [i] based on digital (3, 29, 14)-net over F₄, using
  - net from sequence [i] based on digital (3, 13)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]

(57−25, 57, 29)-Net over F₂ — Digital

Digital (32, 57, 29)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−25, 57, 117)-Net in Base 2 — Upper bound on s

There is no (32, 57, 118)-net in base 2, because

1 times m-reduction [i] would yield (32, 56, 118)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 73431 479596 730022 > 2⁵⁶ [i]