MinT - Best Known (45, 45+48, s)-Nets in Base 9

Best Known (45, 45+48, s)-Nets in Base 9

(45, 45+48, 104)-Net over F₉ — Constructive and digital

Digital (45, 93, 104)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (8, 32, 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 (13, 61, 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]

(45, 45+48, 163)-Net over F₉ — Digital

Digital (45, 93, 163)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+48, 6094)-Net in Base 9 — Upper bound on s

There is no (45, 93, 6095)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55663 763323 758055 744934 774581 055142 282930 977169 466281 360972 273230 303397 361820 962445 972289 > 9⁹³ [i]