MinT - Best Known (69−22, 69, s)-Nets in Base 2

Best Known (69−22, 69, s)-Nets in Base 2

(69−22, 69, 56)-Net over F₂ — Constructive and digital

Digital (47, 69, 56)-net over F₂, using

1 times m-reduction [i] based on digital (47, 70, 56)-net over F₂, using
- trace code for nets [i] based on digital (12, 35, 28)-net over F₄, using
  - net from sequence [i] based on digital (12, 27)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

(69−22, 69, 69)-Net over F₂ — Digital

Digital (47, 69, 69)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(69−22, 69, 363)-Net in Base 2 — Upper bound on s

There is no (47, 69, 364)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 592 567882 740434 968875 > 2⁶⁹ [i]