MinT - Best Known (132−57, 132, s)-Nets in Base 8

Best Known (132−57, 132, s)-Nets in Base 8

(132−57, 132, 354)-Net over F₈ — Constructive and digital

Digital (75, 132, 354)-net over F₈, using

4 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]

(132−57, 132, 418)-Net over F₈ — Digital

Digital (75, 132, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 66, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(132−57, 132, 27089)-Net in Base 8 — Upper bound on s

There is no (75, 132, 27090)-net in base 8, because

1 times m-reduction [i] would yield (75, 131, 27090)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20188 674118 331599 049696 968522 010875 586634 159319 831439 992136 353446 239730 471619 222268 759280 138213 042515 508925 663439 383824 > 8¹³¹ [i]