MinT - Best Known (55, 55+37, s)-Nets in Base 8

Best Known (55, 55+37, s)-Nets in Base 8

(55, 55+37, 354)-Net over F₈ — Constructive and digital

Digital (55, 92, 354)-net over F₈, using

4 times m-reduction [i] based on digital (55, 96, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 48, 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]

(55, 55+37, 424)-Net over F₈ — Digital

Digital (55, 92, 424)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+37, 39676)-Net in Base 8 — Upper bound on s

There is no (55, 92, 39677)-net in base 8, because

1 times m-reduction [i] would yield (55, 91, 39677)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 15181 106638 733060 851099 764120 287315 374488 048151 403462 599303 762660 631860 219191 807602 > 8⁹¹ [i]