MinT - Best Known (108−46, 108, s)-Nets in Base 8

Best Known (108−46, 108, s)-Nets in Base 8

(108−46, 108, 354)-Net over F₈ — Constructive and digital

Digital (62, 108, 354)-net over F₈, using

2 times m-reduction [i] based on digital (62, 110, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 55, 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]

(108−46, 108, 365)-Net over F₈ — Digital

Digital (62, 108, 365)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−46, 108, 23425)-Net in Base 8 — Upper bound on s

There is no (62, 108, 23426)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 34 190548 217500 886572 803816 047859 340757 009948 076313 907117 856920 032199 165425 911898 923955 673482 954432 > 8¹⁰⁸ [i]