MinT - Best Known (77−33, 77, s)-Nets in Base 9

Best Known (77−33, 77, s)-Nets in Base 9

(77−33, 77, 320)-Net over F₉ — Constructive and digital

Digital (44, 77, 320)-net over F₉, using

1 times m-reduction [i] based on digital (44, 78, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 39, 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]

(77−33, 77, 334)-Net over F₉ — Digital

Digital (44, 77, 334)-net over F₉, using

1 times m-reduction [i] based on digital (44, 78, 334)-net over F₉, using
- trace code for nets [i] based on digital (5, 39, 167)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
      - a curve from the manYPoints database [i]

(77−33, 77, 28970)-Net in Base 9 — Upper bound on s

There is no (44, 77, 28971)-net in base 9, because

1 times m-reduction [i] would yield (44, 76, 28971)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 330534 646010 709224 784451 164020 623887 521725 060208 302056 474408 661347 692929 > 9⁷⁶ [i]