MinT - Best Known (96−77, 96, s)-Nets in Base 9

Best Known (96−77, 96, s)-Nets in Base 9

(96−77, 96, 74)-Net over F₉ — Constructive and digital

Digital (19, 96, 74)-net over F₉, using

t-expansion [i] based on digital (17, 96, 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]

(96−77, 96, 84)-Net over F₉ — Digital

Digital (19, 96, 84)-net over F₉, using

net from sequence [i] based on digital (19, 83)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
  - Drinfeld modules of rank 1 [i]

(96−77, 96, 433)-Net in Base 9 — Upper bound on s

There is no (19, 96, 434)-net in base 9, because

1 times m-reduction [i] would yield (19, 95, 434)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 703513 633260 846418 983211 273663 882114 798613 141005 638321 776451 078214 443942 087478 448211 784865 > 9⁹⁵ [i]