MinT - Best Known (166−70, 166, s)-Nets in Base 8

Best Known (166−70, 166, s)-Nets in Base 8

(166−70, 166, 354)-Net over F₈ — Constructive and digital

Digital (96, 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]

(166−70, 166, 547)-Net over F₈ — Digital

Digital (96, 166, 547)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−70, 166, 38119)-Net in Base 8 — Upper bound on s

There is no (96, 166, 38120)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 819064 999941 677858 257087 277325 268170 439550 737267 636589 401052 905876 376365 091567 188018 894489 468421 731829 052809 702976 517491 907819 014119 820463 939663 316727 > 8¹⁶⁶ [i]