MinT - Best Known (49, 49+53, s)-Nets in Base 9

Best Known (49, 49+53, s)-Nets in Base 9

(49, 49+53, 108)-Net over F₉ — Constructive and digital

Digital (49, 102, 108)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 32, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (17, 70, 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]

(49, 49+53, 170)-Net over F₉ — Digital

Digital (49, 102, 170)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+53, 6699)-Net in Base 9 — Upper bound on s

There is no (49, 102, 6700)-net in base 9, because

1 times m-reduction [i] would yield (49, 101, 6700)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 394196 037924 354391 918483 648753 823590 819350 103856 560467 373839 990810 003180 234063 001018 278036 527425 > 9¹⁰¹ [i]