MinT - Best Known (41, 74, s)-Nets in Base 8

Best Known (41, 74, s)-Nets in Base 8

(41, 74, 208)-Net over F₈ — Constructive and digital

Digital (41, 74, 208)-net over F₈, using

2 times m-reduction [i] based on digital (41, 76, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 38, 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]

(41, 74, 258)-Net over F₈ — Digital

Digital (41, 74, 258)-net over F₈, using

trace code for nets [i] based on digital (4, 37, 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]

(41, 74, 12807)-Net in Base 8 — Upper bound on s

There is no (41, 74, 12808)-net in base 8, because

1 times m-reduction [i] would yield (41, 73, 12808)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 843249 084436 009069 659509 080686 504198 277605 388835 742978 519710 992992 > 8⁷³ [i]