MinT - Best Known (13, 13+45, s)-Nets in Base 9

Best Known (13, 13+45, s)-Nets in Base 9

(13, 13+45, 64)-Net over F₉ — Constructive and digital

Digital (13, 58, 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]

(13, 13+45, 322)-Net in Base 9 — Upper bound on s

There is no (13, 58, 323)-net in base 9, because

1 times m-reduction [i] would yield (13, 57, 323)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 508422 176815 013016 436689 640881 516126 371243 703123 181713 > 9⁵⁷ [i]