MinT - Best Known (79, 79+59, s)-Nets in Base 8

Best Known (79, 79+59, s)-Nets in Base 8

(79, 79+59, 354)-Net over F₈ — Constructive and digital

Digital (79, 138, 354)-net over F₈, using

6 times m-reduction [i] based on digital (79, 144, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 72, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(79, 79+59, 450)-Net over F₈ — Digital

Digital (79, 138, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 69, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(79, 79+59, 30767)-Net in Base 8 — Upper bound on s

There is no (79, 138, 30768)-net in base 8, because

1 times m-reduction [i] would yield (79, 137, 30768)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5291 832916 797524 492731 665518 243255 744979 054853 624917 664707 313374 561573 668921 607278 413666 333003 901859 777846 604656 346691 153542 > 8¹³⁷ [i]