MinT - Best Known (61−18, 61, s)-Nets in Base 9

Best Known (61−18, 61, s)-Nets in Base 9

(61−18, 61, 432)-Net over F₉ — Constructive and digital

Digital (43, 61, 432)-net over F₉, using

1 times m-reduction [i] based on digital (43, 62, 432)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 20, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 10, 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 (23, 42, 232)-net over F₉, using
    - trace code for nets [i] based on digital (2, 21, 116)-net over F₈₁, using
      - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(61−18, 61, 2390)-Net over F₉ — Digital

Digital (43, 61, 2390)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(61−18, 61, 1521611)-Net in Base 9 — Upper bound on s

There is no (43, 61, 1521612)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 16173 176885 057480 104552 847175 640177 721117 088243 536419 262305 > 9⁶¹ [i]