MinT - Best Known (49, 100, s)-Nets in Base 9

Best Known (49, 100, s)-Nets in Base 9

(49, 100, 110)-Net over F₉ — Constructive and digital

Digital (49, 100, 110)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (7, 32, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]
2. digital (17, 68, 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, 100, 182)-Net over F₉ — Digital

Digital (49, 100, 182)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 100, 7629)-Net in Base 9 — Upper bound on s

There is no (49, 100, 7630)-net in base 9, because

1 times m-reduction [i] would yield (49, 99, 7630)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29594 165985 512194 781597 406093 057229 442770 456102 643396 665759 262928 012639 233185 738494 480519 343089 > 9⁹⁹ [i]