MinT - Best Known (81−63, 81, s)-Nets in Base 9

Best Known (81−63, 81, s)-Nets in Base 9

(81−63, 81, 74)-Net over F₉ — Constructive and digital

Digital (18, 81, 74)-net over F₉, using

t-expansion [i] based on digital (17, 81, 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]

(81−63, 81, 431)-Net in Base 9 — Upper bound on s

There is no (18, 81, 432)-net in base 9, because

1 times m-reduction [i] would yield (18, 80, 432)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22368 440917 603235 989770 986201 554742 798365 467821 131274 312792 727377 700377 819265 > 9⁸⁰ [i]