MinT - Best Known (53−16, 53, s)-Nets in Base 9

Best Known (53−16, 53, s)-Nets in Base 9

(53−16, 53, 400)-Net over F₉ — Constructive and digital

Digital (37, 53, 400)-net over F₉, using

1 times m-reduction [i] based on digital (37, 54, 400)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 18, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 9, 100)-net over F₈₁, using
      - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
  2. digital (19, 36, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 18, 100)-net over F₈₁, using
      - net from sequence [i] based on digital (1, 99)-sequence over F₈₁ (see above)

(53−16, 53, 1897)-Net over F₉ — Digital

Digital (37, 53, 1897)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−16, 53, 987312)-Net in Base 9 — Upper bound on s

There is no (37, 53, 987313)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 375 711121 920104 930925 197887 971944 597230 956970 228545 > 9⁵³ [i]