MinT - Best Known (121−99, 121, s)-Nets in Base 9

Best Known (121−99, 121, s)-Nets in Base 9

(121−99, 121, 78)-Net over F₉ — Constructive and digital

Digital (22, 121, 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]

(121−99, 121, 88)-Net over F₉ — Digital

Digital (22, 121, 88)-net over F₉, using

t-expansion [i] based on digital (21, 121, 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]

(121−99, 121, 489)-Net in Base 9 — Upper bound on s

There is no (22, 121, 490)-net in base 9, because

1 times m-reduction [i] would yield (22, 120, 490)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 436727 786710 922512 363173 333691 592700 980505 151875 046608 510048 203026 806738 934669 613553 317378 468864 622278 836526 069841 > 9¹²⁰ [i]