MinT - Best Known (62, 125, s)-Nets in Base 9

Best Known (62, 125, s)-Nets in Base 9

(62, 125, 138)-Net over F₉ — Constructive and digital

Digital (62, 125, 138)-net over F₉, using

1 times m-reduction [i] based on digital (62, 126, 138)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 45, 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, 81, 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]

(62, 125, 229)-Net over F₉ — Digital

Digital (62, 125, 229)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 125, 10165)-Net in Base 9 — Upper bound on s

There is no (62, 125, 10166)-net in base 9, because

1 times m-reduction [i] would yield (62, 124, 10166)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21251 077723 257234 531652 407613 766190 155601 770881 682907 032532 873074 556488 752415 406820 776974 423175 174659 915084 837747 855249 > 9¹²⁴ [i]