MinT - Best Known (148−65, 148, s)-Nets in Base 8

Best Known (148−65, 148, s)-Nets in Base 8

(148−65, 148, 354)-Net over F₈ — Constructive and digital

Digital (83, 148, 354)-net over F₈, using

4 times m-reduction [i] based on digital (83, 152, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 76, 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]

(148−65, 148, 418)-Net over F₈ — Digital

Digital (83, 148, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 74, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(148−65, 148, 25704)-Net in Base 8 — Upper bound on s

There is no (83, 148, 25705)-net in base 8, because

1 times m-reduction [i] would yield (83, 147, 25705)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 680332 999993 609210 988831 196353 116295 099314 075334 657646 726656 752875 291652 358737 353181 720821 845718 897883 985484 843683 860799 250413 700547 > 8¹⁴⁷ [i]