MinT - Best Known (169−73, 169, s)-Nets in Base 8

Best Known (169−73, 169, s)-Nets in Base 8

(169−73, 169, 354)-Net over F₈ — Constructive and digital

Digital (96, 169, 354)-net over F₈, using

t-expansion [i] based on digital (93, 169, 354)-net over F₈, using
- 3 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]

(169−73, 169, 499)-Net over F₈ — Digital

Digital (96, 169, 499)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−73, 169, 33401)-Net in Base 8 — Upper bound on s

There is no (96, 169, 33402)-net in base 8, because

1 times m-reduction [i] would yield (96, 168, 33402)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 407810 495354 203843 651288 913470 488211 543674 860557 578599 522258 432353 973219 568241 771365 700718 812840 998736 976446 759656 283032 332205 190177 187307 140899 417250 > 8¹⁶⁸ [i]