MinT - Best Known (89−71, 89, s)-Nets in Base 9

Best Known (89−71, 89, s)-Nets in Base 9

(89−71, 89, 74)-Net over F₉ — Constructive and digital

Digital (18, 89, 74)-net over F₉, using

t-expansion [i] based on digital (17, 89, 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]

(89−71, 89, 414)-Net in Base 9 — Upper bound on s

There is no (18, 89, 415)-net in base 9, because

1 times m-reduction [i] would yield (18, 88, 415)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 951596 729617 442835 171520 418547 913986 749364 012057 538652 370506 766179 074938 550031 911401 > 9⁸⁸ [i]