MinT - Best Known (134−29, 134, s)-Nets in Base 2

Best Known (134−29, 134, s)-Nets in Base 2

(134−29, 134, 195)-Net over F₂ — Constructive and digital

Digital (105, 134, 195)-net over F₂, using

t-expansion [i] based on digital (104, 134, 195)-net over F₂, using
- 1 times m-reduction [i] based on digital (104, 135, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 45, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(134−29, 134, 300)-Net over F₂ — Digital

Digital (105, 134, 300)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−29, 134, 4357)-Net in Base 2 — Upper bound on s

There is no (105, 134, 4358)-net in base 2, because

1 times m-reduction [i] would yield (105, 133, 4358)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10916 576523 392418 486400 742998 104413 741952 > 2¹³³ [i]