MinT - Best Known (61, 61+63, s)-Nets in Base 9

Best Known (61, 61+63, s)-Nets in Base 9

(61, 61+63, 138)-Net over F₉ — Constructive and digital

Digital (61, 124, 138)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 44, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 80, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(61, 61+63, 220)-Net over F₉ — Digital

Digital (61, 124, 220)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+63, 9468)-Net in Base 9 — Upper bound on s

There is no (61, 124, 9469)-net in base 9, because

1 times m-reduction [i] would yield (61, 123, 9469)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2360 422052 439290 178628 697813 806654 079561 679918 083384 842895 508963 707741 508948 917851 394896 625811 636571 871271 520082 850777 > 9¹²³ [i]