MinT - Best Known (40, 60, s)-Nets in Base 8

Best Known (40, 60, s)-Nets in Base 8

(40, 60, 354)-Net over F₈ — Constructive and digital

Digital (40, 60, 354)-net over F₈, using

6 times m-reduction [i] based on digital (40, 66, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 33, 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]

(40, 60, 518)-Net in Base 8 — Constructive

(40, 60, 518)-net in base 8, using

base change [i] based on digital (25, 45, 518)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (25, 46, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 23, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(40, 60, 815)-Net over F₈ — Digital

Digital (40, 60, 815)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 60, 169591)-Net in Base 8 — Upper bound on s

There is no (40, 60, 169592)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 532578 756459 228397 652026 489914 321975 779310 580799 332862 > 8⁶⁰ [i]