MinT - Best Known (95−49, 95, s)-Nets in Base 9

Best Known (95−49, 95, s)-Nets in Base 9

(95−49, 95, 106)-Net over F₉ — Constructive and digital

Digital (46, 95, 106)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 29, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 66, 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]

(95−49, 95, 166)-Net over F₉ — Digital

Digital (46, 95, 166)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−49, 95, 6680)-Net in Base 9 — Upper bound on s

There is no (46, 95, 6681)-net in base 9, because

1 times m-reduction [i] would yield (46, 94, 6681)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 501454 785875 553592 024583 574594 412642 002635 668705 720853 680532 830609 437992 710551 652413 545409 > 9⁹⁴ [i]