MinT - Best Known (158−75, 158, s)-Nets in Base 8

Best Known (158−75, 158, s)-Nets in Base 8

(158−75, 158, 208)-Net over F₈ — Constructive and digital

Digital (83, 158, 208)-net over F₈, using

2 times m-reduction [i] based on digital (83, 160, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 80, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(158−75, 158, 225)-Net in Base 8 — Constructive

(83, 158, 225)-net in base 8, using

14 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
- base change [i] based on digital (40, 129, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(158−75, 158, 316)-Net over F₈ — Digital

Digital (83, 158, 316)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−75, 158, 14194)-Net in Base 8 — Upper bound on s

There is no (83, 158, 14195)-net in base 8, because

1 times m-reduction [i] would yield (83, 157, 14195)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6098 530695 640565 220279 549575 400067 714729 886204 911200 711869 571141 961518 364600 074036 066369 274886 111053 790685 976787 959828 060809 657011 797565 087304 > 8¹⁵⁷ [i]