MinT - Best Known (57−39, 57, s)-Nets in Base 9

Best Known (57−39, 57, s)-Nets in Base 9

(57−39, 57, 74)-Net over F₉ — Constructive and digital

Digital (18, 57, 74)-net over F₉, using

t-expansion [i] based on digital (17, 57, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(57−39, 57, 632)-Net in Base 9 — Upper bound on s

There is no (18, 57, 633)-net in base 9, because

1 times m-reduction [i] would yield (18, 56, 633)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 279562 680586 566429 666308 705014 613119 922359 511249 621913 > 9⁵⁶ [i]