MinT - Best Known (30, 30+13, s)-Nets in Base 9

Best Known (30, 30+13, s)-Nets in Base 9

(30, 30+13, 400)-Net over F₉ — Constructive and digital

Digital (30, 43, 400)-net over F₉, using

9¹ times duplication [i] based on digital (29, 42, 400)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (8, 14, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 7, 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 (15, 28, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 14, 100)-net over F₈₁, using
      - net from sequence [i] based on digital (1, 99)-sequence over F₈₁ (see above)

(30, 30+13, 1742)-Net over F₉ — Digital

Digital (30, 43, 1742)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 30+13, 1789900)-Net in Base 9 — Upper bound on s

There is no (30, 43, 1789901)-net in base 9, because

1 times m-reduction [i] would yield (30, 42, 1789901)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11972 537912 853939 365948 358836 761325 665201 > 9⁴² [i]