MinT - Best Known (64, 64+51, s)-Nets in Base 9

Best Known (64, 64+51, s)-Nets in Base 9

(64, 64+51, 320)-Net over F₉ — Constructive and digital

Digital (64, 115, 320)-net over F₉, using

3 times m-reduction [i] based on digital (64, 118, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 59, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(64, 64+51, 380)-Net over F₉ — Digital

Digital (64, 115, 380)-net over F₉, using

1 times m-reduction [i] based on digital (64, 116, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 58, 190)-net over F₈₁, using
  - net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
      - a curve from the manYPoints database [i]

(64, 64+51, 28552)-Net in Base 9 — Upper bound on s

There is no (64, 115, 28553)-net in base 9, because

1 times m-reduction [i] would yield (64, 114, 28553)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 076402 380486 750344 388257 666243 775894 718440 116402 565751 927949 438545 148596 698007 402085 219977 671902 549243 152905 > 9¹¹⁴ [i]