MinT - Best Known (17, 17+57, s)-Nets in Base 9

Best Known (17, 17+57, s)-Nets in Base 9

(17, 17+57, 74)-Net over F₉ — Constructive and digital

Digital (17, 74, 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]

(17, 17+57, 417)-Net in Base 9 — Upper bound on s

There is no (17, 74, 418)-net in base 9, because

1 times m-reduction [i] would yield (17, 73, 418)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4727 636530 617676 121201 000383 322203 965014 017075 040594 049495 146377 888065 > 9⁷³ [i]