MinT - Best Known (97−69, 97, s)-Nets in Base 9

Best Known (97−69, 97, s)-Nets in Base 9

(97−69, 97, 78)-Net over F₉ — Constructive and digital

Digital (28, 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]

(97−69, 97, 110)-Net over F₉ — Digital

Digital (28, 97, 110)-net over F₉, using

t-expansion [i] based on 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]

(97−69, 97, 816)-Net in Base 9 — Upper bound on s

There is no (28, 97, 817)-net in base 9, because

1 times m-reduction [i] would yield (28, 96, 817)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 508649 473106 782778 841072 442732 409655 582552 410392 905842 551019 552036 046270 306580 539240 538705 > 9⁹⁶ [i]