MinT - Best Known (61, 61+31, s)-Nets in Base 9

Best Known (61, 61+31, s)-Nets in Base 9

(61, 61+31, 448)-Net over F₉ — Constructive and digital

Digital (61, 92, 448)-net over F₉, using

4 times m-reduction [i] based on digital (61, 96, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 48, 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]

(61, 61+31, 1286)-Net over F₉ — Digital

Digital (61, 92, 1286)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+31, 494014)-Net in Base 9 — Upper bound on s

There is no (61, 92, 494015)-net in base 9, because

1 times m-reduction [i] would yield (61, 91, 494015)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 597556 195428 465983 980569 783447 965422 275913 019572 803342 718508 077085 392051 984208 157065 > 9⁹¹ [i]