MinT - Best Known (122−55, 122, s)-Nets in Base 9

Best Known (122−55, 122, s)-Nets in Base 9

(122−55, 122, 320)-Net over F₉ — Constructive and digital

Digital (67, 122, 320)-net over F₉, using

2 times m-reduction [i] based on digital (67, 124, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 62, 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]

(122−55, 122, 380)-Net over F₉ — Digital

Digital (67, 122, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 61, 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]

(122−55, 122, 25790)-Net in Base 9 — Upper bound on s

There is no (67, 122, 25791)-net in base 9, because

1 times m-reduction [i] would yield (67, 121, 25791)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29 075616 503055 149352 385926 727266 204479 803707 580870 564468 108203 427086 376887 822254 974588 696032 553743 191399 129770 711337 > 9¹²¹ [i]