MinT - Best Known (72−29, 72, s)-Nets in Base 8

Best Known (72−29, 72, s)-Nets in Base 8

(72−29, 72, 354)-Net over F₈ — Constructive and digital

Digital (43, 72, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 36, 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]

(72−29, 72, 32824)-Net in Base 8 — Upper bound on s

There is no (43, 72, 32825)-net in base 8, because

1 times m-reduction [i] would yield (43, 71, 32825)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13164 507094 941679 632588 564248 055666 524228 966662 577316 639501 851416 > 8⁷¹ [i]