MinT - Best Known (29−13, 29, s)-Nets in Base 9

Best Known (29−13, 29, s)-Nets in Base 9

(29−13, 29, 200)-Net over F₉ — Constructive and digital

Digital (16, 29, 200)-net over F₉, using

1 times m-reduction [i] based on digital (16, 30, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 15, 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]

(29−13, 29, 10620)-Net in Base 9 — Upper bound on s

There is no (16, 29, 10621)-net in base 9, because

1 times m-reduction [i] would yield (16, 28, 10621)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 523 596858 902988 687561 104049 > 9²⁸ [i]