MinT - Best Known (117−50, 117, s)-Nets in Base 8

Best Known (117−50, 117, s)-Nets in Base 8

(117−50, 117, 354)-Net over F₈ — Constructive and digital

Digital (67, 117, 354)-net over F₈, using

3 times m-reduction [i] based on digital (67, 120, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 60, 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]

(117−50, 117, 384)-Net over F₈ — Digital

Digital (67, 117, 384)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−50, 117, 24474)-Net in Base 8 — Upper bound on s

There is no (67, 117, 24475)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4589 622078 835428 664012 773652 417654 338118 995456 576807 233536 696784 407323 476028 760359 409829 996141 920688 358254 > 8¹¹⁷ [i]