MinT - Best Known (165−72, 165, s)-Nets in Base 8

Best Known (165−72, 165, s)-Nets in Base 8

(165−72, 165, 354)-Net over F₈ — Constructive and digital

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]

(165−72, 165, 468)-Net over F₈ — Digital

Digital (93, 165, 468)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−72, 165, 28083)-Net in Base 8 — Upper bound on s

There is no (93, 165, 28084)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 102356 233882 365455 516743 915284 081293 271114 270403 078788 555304 326824 537846 668242 475604 406638 436725 312213 896557 910747 581697 890059 231845 625277 798737 893676 > 8¹⁶⁵ [i]