MinT - Best Known (79−33, 79, s)-Nets in Base 9

Best Known (79−33, 79, s)-Nets in Base 9

(79−33, 79, 320)-Net over F₉ — Constructive and digital

Digital (46, 79, 320)-net over F₉, using

3 times m-reduction [i] based on digital (46, 82, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 41, 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]

(79−33, 79, 380)-Net over F₉ — Digital

Digital (46, 79, 380)-net over F₉, using

1 times m-reduction [i] based on digital (46, 80, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 40, 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]

(79−33, 79, 38130)-Net in Base 9 — Upper bound on s

There is no (46, 79, 38131)-net in base 9, because

1 times m-reduction [i] would yield (46, 78, 38131)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 269 775297 608101 068752 152275 579309 103977 153158 185436 176275 246027 697772 076417 > 9⁷⁸ [i]