MinT - Best Known (14, 39, s)-Nets in Base 9

Best Known (14, 39, s)-Nets in Base 9

(14, 39, 64)-Net over F₉ — Constructive and digital

Digital (14, 39, 64)-net over F₉, using

t-expansion [i] based on digital (13, 39, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(14, 39, 688)-Net in Base 9 — Upper bound on s

There is no (14, 39, 689)-net in base 9, because

1 times m-reduction [i] would yield (14, 38, 689)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 853063 864101 660254 444092 723165 232865 > 9³⁸ [i]