MinT - Best Known (174, 174+69, s)-Nets in Base 2

Best Known (174, 174+69, s)-Nets in Base 2

(174, 174+69, 144)-Net over F₂ — Constructive and digital

Digital (174, 243, 144)-net over F₂, using

t-expansion [i] based on digital (173, 243, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 81, 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]

(174, 174+69, 241)-Net over F₂ — Digital

Digital (174, 243, 241)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 174+69, 1829)-Net in Base 2 — Upper bound on s

There is no (174, 243, 1830)-net in base 2, because

1 times m-reduction [i] would yield (174, 242, 1830)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 084647 044008 125452 523107 418155 572725 189771 530114 048214 836882 489031 000450 > 2²⁴² [i]