MinT - Best Known (69, 69+46, s)-Nets in Base 2

Best Known (69, 69+46, s)-Nets in Base 2

(69, 69+46, 54)-Net over F₂ — Constructive and digital

Digital (69, 115, 54)-net over F₂, using

3 times m-reduction [i] based on digital (69, 118, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 59, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(69, 69+46, 59)-Net over F₂ — Digital

Digital (69, 115, 59)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+46, 269)-Net in Base 2 — Upper bound on s

There is no (69, 115, 270)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 43603 208728 584734 566928 997822 785152 > 2¹¹⁵ [i]