MinT - Best Known (69−24, 69, s)-Nets in Base 2

Best Known (69−24, 69, s)-Nets in Base 2

(69−24, 69, 54)-Net over F₂ — Constructive and digital

Digital (45, 69, 54)-net over F₂, using

1 times m-reduction [i] based on digital (45, 70, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 35, 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]

(69−24, 69, 56)-Net over F₂ — Digital

Digital (45, 69, 56)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(69−24, 69, 267)-Net in Base 2 — Upper bound on s

There is no (45, 69, 268)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 600 309878 611256 434432 > 2⁶⁹ [i]