MinT - Best Known (166−72, 166, s)-Nets in Base 8

Best Known (166−72, 166, s)-Nets in Base 8

(166−72, 166, 354)-Net over F₈ — Constructive and digital

Digital (94, 166, 354)-net over F₈, using

t-expansion [i] based on digital (93, 166, 354)-net over F₈, using
- 6 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]

(166−72, 166, 483)-Net over F₈ — Digital

Digital (94, 166, 483)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−72, 166, 29754)-Net in Base 8 — Upper bound on s

There is no (94, 166, 29755)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818545 703511 176958 026588 170464 835475 366402 820575 103085 554002 358223 177497 434057 809913 584560 100716 490700 153214 535884 191679 754902 982999 655537 982653 880882 > 8¹⁶⁶ [i]