MinT - Best Known (75, 75+55, s)-Nets in Base 8

Best Known (75, 75+55, s)-Nets in Base 8

(75, 75+55, 354)-Net over F₈ — Constructive and digital

Digital (75, 130, 354)-net over F₈, using

6 times m-reduction [i] based on digital (75, 136, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 68, 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]

(75, 75+55, 450)-Net over F₈ — Digital

Digital (75, 130, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 65, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(75, 75+55, 32199)-Net in Base 8 — Upper bound on s

There is no (75, 130, 32200)-net in base 8, because

1 times m-reduction [i] would yield (75, 129, 32200)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 315 434306 800470 794827 240898 563711 741425 982916 426374 367898 291479 341697 789529 271103 270561 502670 523962 408676 749765 043592 > 8¹²⁹ [i]