MinT - Best Known (117−51, 117, s)-Nets in Base 8

Best Known (117−51, 117, s)-Nets in Base 8

(117−51, 117, 354)-Net over F₈ — Constructive and digital

Digital (66, 117, 354)-net over F₈, using

1 times m-reduction [i] based on digital (66, 118, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 59, 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]

(117−51, 117, 22519)-Net in Base 8 — Upper bound on s

There is no (66, 117, 22520)-net in base 8, because

1 times m-reduction [i] would yield (66, 116, 22520)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 573 479753 555450 566335 831431 029600 875319 499394 425575 232395 267038 477561 009703 506365 216108 686176 582839 821308 > 8¹¹⁶ [i]