MinT - Best Known (124−89, 124, s)-Nets in Base 9

Best Known (124−89, 124, s)-Nets in Base 9

(124−89, 124, 81)-Net over F₉ — Constructive and digital

Digital (35, 124, 81)-net over F₉, using

t-expansion [i] based on digital (32, 124, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(124−89, 124, 128)-Net over F₉ — Digital

Digital (35, 124, 128)-net over F₉, using

t-expansion [i] based on digital (33, 124, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(124−89, 124, 976)-Net in Base 9 — Upper bound on s

There is no (35, 124, 977)-net in base 9, because

1 times m-reduction [i] would yield (35, 123, 977)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2418 994294 970847 242983 068585 169428 827178 539913 401827 700446 616817 628176 753223 354311 323644 171096 408961 501102 396861 304801 > 9¹²³ [i]