MinT - Best Known (109−45, 109, s)-Nets in Base 9

Best Known (109−45, 109, s)-Nets in Base 9

(109−45, 109, 344)-Net over F₉ — Constructive and digital

Digital (64, 109, 344)-net over F₉, using

5 times m-reduction [i] based on digital (64, 114, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 57, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(109−45, 109, 504)-Net over F₉ — Digital

Digital (64, 109, 504)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−45, 109, 54716)-Net in Base 9 — Upper bound on s

There is no (64, 109, 54717)-net in base 9, because

1 times m-reduction [i] would yield (64, 108, 54717)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 434480 977496 734020 067612 573027 291606 230420 209296 044274 357550 577985 108660 065747 217716 582293 288572 383025 > 9¹⁰⁸ [i]