MinT - Best Known (129, 198, s)-Nets in Base 2

Best Known (129, 198, s)-Nets in Base 2

Digital (129, 198, 75)-net over F₂, using

(129, 198, 86)-net in base 2, using

trace code for nets [i] based on (30, 99, 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 (129, 198, 125)-net over F₂, using

There is no (129, 198, 703)-net in base 2, because

1 times m-reduction [i] would yield (129, 197, 703)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 209560 831871 637419 974799 505584 945876 942096 854066 167184 887065 > 2¹⁹⁷ [i]