MinT - Best Known (172−73, 172, s)-Nets in Base 8

Best Known (172−73, 172, s)-Nets in Base 8

(172−73, 172, 354)-Net over F₈ — Constructive and digital

Digital (99, 172, 354)-net over F₈, using

t-expansion [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]

(172−73, 172, 548)-Net over F₈ — Digital

Digital (99, 172, 548)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−73, 172, 39725)-Net in Base 8 — Upper bound on s

There is no (99, 172, 39726)-net in base 8, because

1 times m-reduction [i] would yield (99, 171, 39726)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26828 458675 282180 097652 047230 136980 108627 469857 709810 302696 882312 588720 055999 222339 815573 681382 378903 282646 342964 344148 176456 188711 083891 333422 903123 742167 > 8¹⁷¹ [i]