MinT - Best Known (51, 51+42, s)-Nets in Base 8

Best Known (51, 51+42, s)-Nets in Base 8

Digital (51, 93, 208)-net over F₈, using

3 times m-reduction [i] based on digital (51, 96, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 48, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

Digital (51, 93, 258)-net over F₈, using

1 times m-reduction [i] based on digital (51, 94, 258)-net over F₈, using
- trace code for nets [i] based on digital (4, 47, 129)-net over F₆₄, using
  - net from sequence [i] based on digital (4, 128)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 4 and N(F) ≥ 129, using
      - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

There is no (51, 93, 12370)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 972870 717623 457997 544820 816544 288848 991020 278159 387881 189563 201686 343163 041923 805648 > 8⁹³ [i]