MinT - Best Known (52−16, 52, s)-Nets in Base 9

Best Known (52−16, 52, s)-Nets in Base 9

(52−16, 52, 400)-Net over F₉ — Constructive and digital

Digital (36, 52, 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 (18, 34, 200)-net over F₉, using
  - trace code for nets [i] based on digital (1, 17, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁ (see above)

(52−16, 52, 1639)-Net over F₉ — Digital

Digital (36, 52, 1639)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(52−16, 52, 750194)-Net in Base 9 — Upper bound on s

There is no (36, 52, 750195)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 745871 826967 510105 184547 336962 609645 729000 128193 > 9⁵² [i]