MinT - Best Known (225−63, 225, s)-Nets in Base 2

Best Known (225−63, 225, s)-Nets in Base 2

(225−63, 225, 144)-Net over F₂ — Constructive and digital

Digital (162, 225, 144)-net over F₂, using

t-expansion [i] based on digital (161, 225, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 75, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(225−63, 225, 233)-Net over F₂ — Digital

Digital (162, 225, 233)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−63, 225, 1813)-Net in Base 2 — Upper bound on s

There is no (162, 225, 1814)-net in base 2, because

1 times m-reduction [i] would yield (162, 224, 1814)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 299723 492204 995749 743445 463787 336942 970758 718571 248838 036644 806400 > 2²²⁴ [i]