MinT - Best Known (89−67, 89, s)-Nets in Base 9

Best Known (89−67, 89, s)-Nets in Base 9

(89−67, 89, 78)-Net over F₉ — Constructive and digital

Digital (22, 89, 78)-net over F₉, using

net from sequence [i] based on digital (22, 77)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
  - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(89−67, 89, 88)-Net over F₉ — Digital

Digital (22, 89, 88)-net over F₉, using

t-expansion [i] based on digital (21, 89, 88)-net over F₉, using
- net from sequence [i] based on digital (21, 87)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
    - a curve from the manYPoints database [i]

(89−67, 89, 556)-Net in Base 9 — Upper bound on s

There is no (22, 89, 557)-net in base 9, because

1 times m-reduction [i] would yield (22, 88, 557)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 955237 497902 299252 032756 275552 268695 751545 228597 918978 306469 968738 672395 543744 760425 > 9⁸⁸ [i]