MinT - Best Known (61, 61+35, s)-Nets in Base 9

Best Known (61, 61+35, s)-Nets in Base 9

(61, 61+35, 448)-Net over F₉ — Constructive and digital

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+35, 854)-Net over F₉ — Digital

Digital (61, 96, 854)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+35, 192914)-Net in Base 9 — Upper bound on s

There is no (61, 96, 192915)-net in base 9, because

1 times m-reduction [i] would yield (61, 95, 192915)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 498530 743049 471233 995261 721569 704608 340268 402504 677198 223532 812166 567218 885964 524656 652825 > 9⁹⁵ [i]