MinT - Best Known (54, 54+40, s)-Nets in Base 9

Best Known (54, 54+40, s)-Nets in Base 9

(54, 54+40, 344)-Net over F₉ — Constructive and digital

Digital (54, 94, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 47, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(54, 54+40, 388)-Net over F₉ — Digital

Digital (54, 94, 388)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+40, 31695)-Net in Base 9 — Upper bound on s

There is no (54, 94, 31696)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 500094 109347 586072 650775 322319 250567 010533 950201 227419 323893 270006 218888 560145 572852 231681 > 9⁹⁴ [i]