MinT - Best Known (63−27, 63, s)-Nets in Base 9

Best Known (63−27, 63, s)-Nets in Base 9

(63−27, 63, 300)-Net over F₉ — Constructive and digital

Digital (36, 63, 300)-net over F₉, using

1 times m-reduction [i] based on digital (36, 64, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 32, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(63−27, 63, 308)-Net over F₉ — Digital

Digital (36, 63, 308)-net over F₉, using

1 times m-reduction [i] based on digital (36, 64, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 32, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(63−27, 63, 25187)-Net in Base 9 — Upper bound on s

There is no (36, 63, 25188)-net in base 9, because

1 times m-reduction [i] would yield (36, 62, 25188)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 145584 829193 916036 100001 124032 025601 539550 456287 165736 084385 > 9⁶² [i]