MinT - Best Known (149−47, 149, s)-Nets in Base 9

Best Known (149−47, 149, s)-Nets in Base 9

(149−47, 149, 750)-Net over F₉ — Constructive and digital

Digital (102, 149, 750)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 23, 10)-net over F₉, using
  - net from sequence [i] based on digital (0, 9)-sequence over F₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 0 and N(F) ≥ 10, using
      - the rational function field F₉(x) [i]
    - Niederreiter sequence [i]
2. digital (79, 126, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 63, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(149−47, 149, 2797)-Net over F₉ — Digital

Digital (102, 149, 2797)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−47, 149, 1628192)-Net in Base 9 — Upper bound on s

There is no (102, 149, 1628193)-net in base 9, because

1 times m-reduction [i] would yield (102, 148, 1628193)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1690 035037 993816 230922 441142 971463 307504 754841 495892 552850 915234 437026 399955 577022 473108 485164 502787 687087 492050 787792 079866 175590 982270 294265 > 9¹⁴⁸ [i]