MinT - Best Known (99−77, 99, s)-Nets in Base 9

Best Known (99−77, 99, s)-Nets in Base 9

(99−77, 99, 78)-Net over F₉ — Constructive and digital

Digital (22, 99, 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]

(99−77, 99, 88)-Net over F₉ — Digital

Digital (22, 99, 88)-net over F₉, using

t-expansion [i] based on digital (21, 99, 88)-net over F₉, using
- net from sequence [i] based on digital (21, 87)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
    - a curve from the manYPoints database [i]

(99−77, 99, 519)-Net in Base 9 — Upper bound on s

There is no (22, 99, 520)-net in base 9, because

1 times m-reduction [i] would yield (22, 98, 520)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3312 369266 682464 710428 214353 885320 321659 050364 299147 339828 498035 474324 370983 201050 746193 576065 > 9⁹⁸ [i]