MinT - Best Known (168−71, 168, s)-Nets in Base 8

Best Known (168−71, 168, s)-Nets in Base 8

(168−71, 168, 354)-Net over F₈ — Constructive and digital

Digital (97, 168, 354)-net over F₈, using

t-expansion [i] based on digital (93, 168, 354)-net over F₈, using
- 4 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(168−71, 168, 547)-Net over F₈ — Digital

Digital (97, 168, 547)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−71, 168, 40453)-Net in Base 8 — Upper bound on s

There is no (97, 168, 40454)-net in base 8, because

1 times m-reduction [i] would yield (97, 167, 40454)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 548064 237779 378383 672664 518672 182417 461255 853049 157889 325794 008495 354108 841830 178843 767584 301306 485386 863166 694497 828969 057485 755628 512992 438670 099296 > 8¹⁶⁷ [i]