MinT - Best Known (81−34, 81, s)-Nets in Base 9

Best Known (81−34, 81, s)-Nets in Base 9

(81−34, 81, 320)-Net over F₉ — Constructive and digital

Digital (47, 81, 320)-net over F₉, using

3 times m-reduction [i] based on digital (47, 84, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 42, 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]

(81−34, 81, 380)-Net over F₉ — Digital

Digital (47, 81, 380)-net over F₉, using

1 times m-reduction [i] based on digital (47, 82, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 41, 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]

(81−34, 81, 31579)-Net in Base 9 — Upper bound on s

There is no (47, 81, 31580)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 196713 374253 060189 400192 765486 191833 856639 425981 621957 262294 312328 343238 227169 > 9⁸¹ [i]