MinT - Best Known (63−27, 63, s)-Nets in Base 8

Best Known (63−27, 63, s)-Nets in Base 8

Digital (36, 63, 208)-net over F₈, using

3 times m-reduction [i] based on digital (36, 66, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 33, 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 (36, 63, 258)-net over F₈, using

1 times m-reduction [i] based on digital (36, 64, 258)-net over F₈, using
- trace code for nets [i] based on digital (4, 32, 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 (36, 63, 16412)-net in base 8, because

1 times m-reduction [i] would yield (36, 62, 16412)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 98 128612 198504 210156 832637 578845 075273 157580 224473 644612 > 8⁶² [i]