MinT - Best Known (76−33, 76, s)-Nets in Base 9

Best Known (76−33, 76, s)-Nets in Base 9

(76−33, 76, 320)-Net over F₉ — Constructive and digital

Digital (43, 76, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 38, 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]

(76−33, 76, 334)-Net over F₉ — Digital

Digital (43, 76, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 38, 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]

(76−33, 76, 25252)-Net in Base 9 — Upper bound on s

There is no (43, 76, 25253)-net in base 9, because

1 times m-reduction [i] would yield (43, 75, 25253)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 370204 013770 940272 100944 810869 777383 096357 760025 468881 746868 586879 374465 > 9⁷⁵ [i]