MinT - Best Known (134−107, 134, s)-Nets in Base 9

Best Known (134−107, 134, s)-Nets in Base 9

(134−107, 134, 78)-Net over F₉ — Constructive and digital

Digital (27, 134, 78)-net over F₉, using

t-expansion [i] based on digital (22, 134, 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]

(134−107, 134, 110)-Net over F₉ — Digital

Digital (27, 134, 110)-net over F₉, using

t-expansion [i] based on digital (26, 134, 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]

(134−107, 134, 606)-Net in Base 9 — Upper bound on s

There is no (27, 134, 607)-net in base 9, because

1 times m-reduction [i] would yield (27, 133, 607)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 506197 436344 142439 845637 144319 952331 593033 945135 008051 875650 499136 724929 573918 152049 121775 270765 317237 571145 338832 070224 319833 > 9¹³³ [i]