MinT - Best Known (64−39, 64, s)-Nets in Base 9

Best Known (64−39, 64, s)-Nets in Base 9

(64−39, 64, 78)-Net over F₉ — Constructive and digital

Digital (25, 64, 78)-net over F₉, using

t-expansion [i] based on digital (22, 64, 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]

(64−39, 64, 96)-Net over F₉ — Digital

Digital (25, 64, 96)-net over F₉, using

net from sequence [i] based on digital (25, 95)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 25 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(64−39, 64, 1434)-Net in Base 9 — Upper bound on s

There is no (25, 64, 1435)-net in base 9, because

1 times m-reduction [i] would yield (25, 63, 1435)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 314615 653622 576236 045154 878889 002450 980474 477047 077535 813513 > 9⁶³ [i]