MinT - Best Known (129, 129+45, s)-Nets in Base 2

Best Known (129, 129+45, s)-Nets in Base 2

(129, 129+45, 144)-Net over F₂ — Constructive and digital

Digital (129, 174, 144)-net over F₂, using

3 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]

(129, 129+45, 229)-Net over F₂ — Digital

Digital (129, 174, 229)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 129+45, 2076)-Net in Base 2 — Upper bound on s

There is no (129, 174, 2077)-net in base 2, because

1 times m-reduction [i] would yield (129, 173, 2077)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12026 991431 260871 819625 230482 327234 336703 786489 653088 > 2¹⁷³ [i]