MinT - Best Known (134−41, 134, s)-Nets in Base 2

Best Known (134−41, 134, s)-Nets in Base 2

(134−41, 134, 72)-Net over F₂ — Constructive and digital

Digital (93, 134, 72)-net over F₂, using

1 times m-reduction [i] based on digital (93, 135, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 45, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(134−41, 134, 123)-Net over F₂ — Digital

Digital (93, 134, 123)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−41, 134, 804)-Net in Base 2 — Upper bound on s

There is no (93, 134, 805)-net in base 2, because

1 times m-reduction [i] would yield (93, 133, 805)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10903 101463 551456 943298 872575 495567 813886 > 2¹³³ [i]