MinT - Best Known (101−75, 101, s)-Nets in Base 9

Best Known (101−75, 101, s)-Nets in Base 9

(101−75, 101, 78)-Net over F₉ — Constructive and digital

Digital (26, 101, 78)-net over F₉, using

t-expansion [i] based on digital (22, 101, 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]

(101−75, 101, 110)-Net over F₉ — Digital

Digital (26, 101, 110)-net over F₉, using

net from sequence [i] based on digital (26, 109)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
  - a curve from the manYPoints database [i]

(101−75, 101, 672)-Net in Base 9 — Upper bound on s

There is no (26, 101, 673)-net in base 9, because

1 times m-reduction [i] would yield (26, 100, 673)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 274493 825919 097181 569277 492408 210982 334590 413552 156080 485122 267965 844237 808224 066309 925297 523881 > 9¹⁰⁰ [i]