MinT - Best Known (152−65, 152, s)-Nets in Base 8

Best Known (152−65, 152, s)-Nets in Base 8

(152−65, 152, 354)-Net over F₈ — Constructive and digital

Digital (87, 152, 354)-net over F₈, using

8 times m-reduction [i] based on digital (87, 160, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 80, 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]

(152−65, 152, 476)-Net over F₈ — Digital

Digital (87, 152, 476)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−65, 152, 33340)-Net in Base 8 — Upper bound on s

There is no (87, 152, 33341)-net in base 8, because

1 times m-reduction [i] would yield (87, 151, 33341)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23261 818984 993636 801825 703384 648941 275598 620594 825492 361149 417349 774725 611665 710499 808753 401375 083458 714391 627201 180139 632382 085629 936419 > 8¹⁵¹ [i]