MinT - Best Known (60, 60+61, s)-Nets in Base 9

Best Known (60, 60+61, s)-Nets in Base 9

(60, 60+61, 138)-Net over F₉ — Constructive and digital

Digital (60, 121, 138)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 43, 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, 78, 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]

(60, 60+61, 223)-Net over F₉ — Digital

Digital (60, 121, 223)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+61, 9859)-Net in Base 9 — Upper bound on s

There is no (60, 121, 9860)-net in base 9, because

1 times m-reduction [i] would yield (60, 120, 9860)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 231668 236720 417016 671492 987701 760821 483293 627879 957346 093817 369257 164624 369429 837925 896835 422170 192296 562570 697537 > 9¹²⁰ [i]