MinT - Best Known (81, 115, s)-Nets in Base 9

Best Known (81, 115, s)-Nets in Base 9

(81, 115, 740)-Net over F₉ — Constructive and digital

Digital (81, 115, 740)-net over F₉, using

15 times m-reduction [i] based on digital (81, 130, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 65, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(81, 115, 3497)-Net over F₉ — Digital

Digital (81, 115, 3497)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 115, 2558723)-Net in Base 9 — Upper bound on s

There is no (81, 115, 2558724)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 54 687617 599895 542359 064086 183207 329625 512519 995346 293914 879572 669372 609261 197223 928738 416249 449074 345185 029665 > 9¹¹⁵ [i]