MinT - Best Known (93−75, 93, s)-Nets in Base 9

Best Known (93−75, 93, s)-Nets in Base 9

(93−75, 93, 74)-Net over F₉ — Constructive and digital

Digital (18, 93, 74)-net over F₉, using

t-expansion [i] based on digital (17, 93, 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]

(93−75, 93, 409)-Net in Base 9 — Upper bound on s

There is no (18, 93, 410)-net in base 9, because

1 times m-reduction [i] would yield (18, 92, 410)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6295 526873 831586 078437 547191 285134 036708 844249 529938 114942 515637 304449 207227 742532 903825 > 9⁹² [i]