MinT - Best Known (137−42, 137, s)-Nets in Base 2

Best Known (137−42, 137, s)-Nets in Base 2

(137−42, 137, 72)-Net over F₂ — Constructive and digital

Digital (95, 137, 72)-net over F₂, using

1 times m-reduction [i] based on digital (95, 138, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 46, 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]

(137−42, 137, 124)-Net over F₂ — Digital

Digital (95, 137, 124)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−42, 137, 768)-Net in Base 2 — Upper bound on s

There is no (95, 137, 769)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 178004 251761 544430 250334 839967 088869 480320 > 2¹³⁷ [i]