MinT - Best Known (15, 56, s)-Nets in Base 9

Best Known (15, 56, s)-Nets in Base 9

(15, 56, 64)-Net over F₉ — Constructive and digital

Digital (15, 56, 64)-net over F₉, using

t-expansion [i] based on digital (13, 56, 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]

(15, 56, 424)-Net in Base 9 — Upper bound on s

There is no (15, 56, 425)-net in base 9, because

1 times m-reduction [i] would yield (15, 55, 425)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 30433 519112 463212 329989 973313 379127 883254 138067 313441 > 9⁵⁵ [i]