MinT - Best Known (88, 88+67, s)-Nets in Base 8

Best Known (88, 88+67, s)-Nets in Base 8

(88, 88+67, 354)-Net over F₈ — Constructive and digital

Digital (88, 155, 354)-net over F₈, using

7 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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]

(88, 88+67, 462)-Net over F₈ — Digital

Digital (88, 155, 462)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+67, 30788)-Net in Base 8 — Upper bound on s

There is no (88, 155, 30789)-net in base 8, because

1 times m-reduction [i] would yield (88, 154, 30789)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 919026 567234 415219 371051 043708 628358 133857 252574 134155 767534 937412 027092 271773 552059 966415 510516 928414 608907 315812 292124 762056 167257 978200 > 8¹⁵⁴ [i]