MinT - Best Known (81, 117, s)-Nets in Base 9

Best Known (81, 117, s)-Nets in Base 9

(81, 117, 740)-Net over F₉ — Constructive and digital

Digital (81, 117, 740)-net over F₉, using

13 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, 117, 2709)-Net over F₉ — Digital

Digital (81, 117, 2709)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 117, 1505266)-Net in Base 9 — Upper bound on s

There is no (81, 117, 1505267)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4429 740706 030142 244806 228469 210073 104437 568270 094511 122005 643813 865543 957140 992071 123656 342399 046139 539694 067761 > 9¹¹⁷ [i]