MinT - Best Known (70, 70+43, s)-Nets in Base 9

Best Known (70, 70+43, s)-Nets in Base 9

(70, 70+43, 448)-Net over F₉ — Constructive and digital

Digital (70, 113, 448)-net over F₉, using

1 times m-reduction [i] based on digital (70, 114, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 57, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(70, 70+43, 783)-Net over F₉ — Digital

Digital (70, 113, 783)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+43, 133246)-Net in Base 9 — Upper bound on s

There is no (70, 113, 133247)-net in base 9, because

1 times m-reduction [i] would yield (70, 112, 133247)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75026 746441 741720 130823 646781 178170 028027 453280 305735 067853 903081 305491 607030 040593 663475 547389 675370 804057 > 9¹¹² [i]