MinT - Best Known (52, 52+54, s)-Nets in Base 9

Best Known (52, 52+54, s)-Nets in Base 9

(52, 52+54, 114)-Net over F₉ — Constructive and digital

Digital (52, 106, 114)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (8, 35, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]
2. digital (17, 71, 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]

(52, 52+54, 191)-Net over F₉ — Digital

Digital (52, 106, 191)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+54, 7597)-Net in Base 9 — Upper bound on s

There is no (52, 106, 7598)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141434 648625 408899 329885 148893 759683 563751 785201 033393 278058 309490 479502 327975 191665 062970 730019 800209 > 9¹⁰⁶ [i]