MinT - Best Known (168−73, 168, s)-Nets in Base 8

Best Known (168−73, 168, s)-Nets in Base 8

(168−73, 168, 354)-Net over F₈ — Constructive and digital

Digital (95, 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]

(168−73, 168, 484)-Net over F₈ — Digital

Digital (95, 168, 484)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−73, 168, 31525)-Net in Base 8 — Upper bound on s

There is no (95, 168, 31526)-net in base 8, because

1 times m-reduction [i] would yield (95, 167, 31526)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 550830 632668 053662 468529 460672 669444 732431 811184 864199 119202 030480 234818 437188 091529 462905 168677 792022 897869 349666 222733 312711 341288 861557 972253 488045 > 8¹⁶⁷ [i]