MinT - Best Known (97−71, 97, s)-Nets in Base 9

Best Known (97−71, 97, s)-Nets in Base 9

(97−71, 97, 78)-Net over F₉ — Constructive and digital

Digital (26, 97, 78)-net over F₉, using

t-expansion [i] based on digital (22, 97, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(97−71, 97, 110)-Net over F₉ — Digital

Digital (26, 97, 110)-net over F₉, using

net from sequence [i] based on digital (26, 109)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
  - a curve from the manYPoints database [i]

(97−71, 97, 699)-Net in Base 9 — Upper bound on s

There is no (26, 97, 700)-net in base 9, because

1 times m-reduction [i] would yield (26, 96, 700)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 42 234282 486673 922776 836939 707661 877681 861747 225895 833835 734313 066856 671553 012102 519462 246945 > 9⁹⁶ [i]