MinT - Best Known (171−75, 171, s)-Nets in Base 8

Best Known (171−75, 171, s)-Nets in Base 8

(171−75, 171, 354)-Net over F₈ — Constructive and digital

Digital (96, 171, 354)-net over F₈, using

t-expansion [i] based on digital (93, 171, 354)-net over F₈, using
- 1 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(171−75, 171, 473)-Net over F₈ — Digital

Digital (96, 171, 473)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−75, 171, 29498)-Net in Base 8 — Upper bound on s

There is no (96, 171, 29499)-net in base 8, because

1 times m-reduction [i] would yield (96, 170, 29499)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3353 024874 381569 409869 524764 304041 384237 614176 979782 770636 352974 535151 238451 946330 567075 282622 004674 126829 614276 411663 345827 576406 961881 422982 490098 628212 > 8¹⁷⁰ [i]