MinT - Best Known (99−81, 99, s)-Nets in Base 9

Best Known (99−81, 99, s)-Nets in Base 9

(99−81, 99, 74)-Net over F₉ — Constructive and digital

Digital (18, 99, 74)-net over F₉, using

t-expansion [i] based on digital (17, 99, 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]

(99−81, 99, 405)-Net in Base 9 — Upper bound on s

There is no (18, 99, 406)-net in base 9, because

1 times m-reduction [i] would yield (18, 98, 406)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3586 673987 410192 935743 904351 268626 814923 070250 032467 568548 141825 544444 857945 262119 947164 856961 > 9⁹⁸ [i]