MinT - Best Known (190−69, 190, s)-Nets in Base 2

Best Known (190−69, 190, s)-Nets in Base 2

Digital (121, 190, 68)-net over F₂, using

10 times m-reduction [i] based on digital (121, 200, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 100, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(121, 190, 72)-net in base 2, using

trace code for nets [i] based on (26, 95, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
  - base expansion [i] based on digital (52, 35)-sequence over F₂, using
    - t-expansion [i] based on digital (51, 35)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 41, N(F)Â =Â 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F₂ with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]

Digital (121, 190, 110)-net over F₂, using

There is no (121, 190, 590)-net in base 2, because

1 times m-reduction [i] would yield (121, 189, 590)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 814 851089 925621 039033 700944 342191 899744 846034 185200 907380 > 2¹⁸⁹ [i]