MinT - Best Known (131−105, 131, s)-Nets in Base 9

Best Known (131−105, 131, s)-Nets in Base 9

(131−105, 131, 78)-Net over F₉ — Constructive and digital

Digital (26, 131, 78)-net over F₉, using

t-expansion [i] based on digital (22, 131, 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]

(131−105, 131, 110)-Net over F₉ — Digital

Digital (26, 131, 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]

(131−105, 131, 582)-Net in Base 9 — Upper bound on s

There is no (26, 131, 583)-net in base 9, because

1 times m-reduction [i] would yield (26, 130, 583)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11429 279232 238442 219494 084250 775608 989514 430067 423140 515338 471026 043419 510772 735824 162518 202380 818277 129838 419128 865695 778145 > 9¹³⁰ [i]