MinT - Best Known (55, 55+45, s)-Nets in Base 9

Best Known (55, 55+45, s)-Nets in Base 9

(55, 55+45, 320)-Net over F₉ — Constructive and digital

Digital (55, 100, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 50, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(55, 55+45, 334)-Net over F₉ — Digital

Digital (55, 100, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 50, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(55, 55+45, 22263)-Net in Base 9 — Upper bound on s

There is no (55, 100, 22264)-net in base 9, because

1 times m-reduction [i] would yield (55, 99, 22264)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29523 431803 583700 113042 282518 335801 075208 327603 804425 785106 716433 466129 922911 134347 355909 102465 > 9⁹⁹ [i]