MinT - Best Known (165−69, 165, s)-Nets in Base 8

Best Known (165−69, 165, s)-Nets in Base 8

(165−69, 165, 354)-Net over F₈ — Constructive and digital

Digital (96, 165, 354)-net over F₈, using

t-expansion [i] based on digital (93, 165, 354)-net over F₈, using
- 7 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]

(165−69, 165, 564)-Net over F₈ — Digital

Digital (96, 165, 564)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−69, 165, 43878)-Net in Base 8 — Upper bound on s

There is no (96, 165, 43879)-net in base 8, because

1 times m-reduction [i] would yield (96, 164, 43879)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12796 214191 649922 698001 588396 690702 304335 075543 211319 541992 870978 019568 150453 415157 200308 621764 696965 367407 315349 582236 343135 154390 073338 515569 699617 > 8¹⁶⁴ [i]