MinT - Best Known (175−45, 175, s)-Nets in Base 2

Best Known (175−45, 175, s)-Nets in Base 2

(175−45, 175, 144)-Net over F₂ — Constructive and digital

Digital (130, 175, 144)-net over F₂, using

t-expansion [i] based on digital (129, 175, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (129, 177, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 59, 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]

(175−45, 175, 233)-Net over F₂ — Digital

Digital (130, 175, 233)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−45, 175, 2144)-Net in Base 2 — Upper bound on s

There is no (130, 175, 2145)-net in base 2, because

1 times m-reduction [i] would yield (130, 174, 2145)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24174 069946 539753 930999 709010 836020 691459 846769 409712 > 2¹⁷⁴ [i]