MinT - Best Known (125, 125+65, s)-Nets in Base 2

Best Known (125, 125+65, s)-Nets in Base 2

Digital (125, 190, 75)-net over F₂, using

(125, 190, 86)-net in base 2, using

trace code for nets [i] based on (30, 95, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
  - base expansion [i] based on digital (60, 42)-sequence over F₂, using
    - t-expansion [i] based on digital (59, 42)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

Digital (125, 190, 126)-net over F₂, using

There is no (125, 190, 721)-net in base 2, because

1 times m-reduction [i] would yield (125, 189, 721)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 788 652715 140923 474060 655835 302501 098189 667931 094742 877430 > 2¹⁸⁹ [i]