MinT - Best Known (134−41, 134, s)-Nets in Base 9

Best Known (134−41, 134, s)-Nets in Base 9

(134−41, 134, 750)-Net over F₉ — Constructive and digital

Digital (93, 134, 750)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 20, 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 (73, 114, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 57, 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]

(134−41, 134, 3120)-Net over F₉ — Digital

Digital (93, 134, 3120)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−41, 134, 2301053)-Net in Base 9 — Upper bound on s

There is no (93, 134, 2301054)-net in base 9, because

1 times m-reduction [i] would yield (93, 133, 2301054)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 208364 465853 925423 754847 844651 759640 285947 064383 457467 231399 051440 940276 482428 114824 313713 872839 450799 642169 219722 347554 889281 > 9¹³³ [i]