MinT - Best Known (145−117, 145, s)-Nets in Base 9

Best Known (145−117, 145, s)-Nets in Base 9

(145−117, 145, 78)-Net over F₉ — Constructive and digital

Digital (28, 145, 78)-net over F₉, using

t-expansion [i] based on digital (22, 145, 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]

(145−117, 145, 110)-Net over F₉ — Digital

Digital (28, 145, 110)-net over F₉, using

t-expansion [i] based on digital (26, 145, 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]

(145−117, 145, 621)-Net in Base 9 — Upper bound on s

There is no (28, 145, 622)-net in base 9, because

1 times m-reduction [i] would yield (28, 144, 622)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 271841 860648 227227 580246 429751 514069 618009 902758 534496 096421 795731 561706 498958 375228 265912 448056 315991 845801 810902 720638 958334 324931 441313 > 9¹⁴⁴ [i]