MinT - Best Known (92−67, 92, s)-Nets in Base 9

Best Known (92−67, 92, s)-Nets in Base 9

(92−67, 92, 78)-Net over F₉ — Constructive and digital

Digital (25, 92, 78)-net over F₉, using

t-expansion [i] based on digital (22, 92, 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]

(92−67, 92, 96)-Net over F₉ — Digital

Digital (25, 92, 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]

(92−67, 92, 684)-Net in Base 9 — Upper bound on s

There is no (25, 92, 685)-net in base 9, because

1 times m-reduction [i] would yield (25, 91, 685)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 712 288086 102420 577671 891328 333405 839911 017828 837181 179035 636083 810037 739539 556784 524905 > 9⁹¹ [i]