MinT - Best Known (69, 69+20, s)-Nets in Base 2

Best Known (69, 69+20, s)-Nets in Base 2

(69, 69+20, 135)-Net over F₂ — Constructive and digital

Digital (69, 89, 135)-net over F₂, using

1 times m-reduction [i] based on digital (69, 90, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 30, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(69, 69+20, 203)-Net over F₂ — Digital

Digital (69, 89, 203)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+20, 2148)-Net in Base 2 — Upper bound on s

There is no (69, 89, 2149)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 619 040316 561120 525346 453416 > 2⁸⁹ [i]