MinT - Best Known (84−37, 84, s)-Nets in Base 9

Best Known (84−37, 84, s)-Nets in Base 9

(84−37, 84, 320)-Net over F₉ — Constructive and digital

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]

(84−37, 84, 334)-Net over F₉ — Digital

Digital (47, 84, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 42, 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]

(84−37, 84, 23711)-Net in Base 9 — Upper bound on s

There is no (47, 84, 23712)-net in base 9, because

1 times m-reduction [i] would yield (47, 83, 23712)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 931212 763604 812450 748116 298804 034176 907639 357317 748330 942177 062224 007263 030785 > 9⁸³ [i]