MinT - Best Known (56, 56+30, s)-Nets in Base 9

Best Known (56, 56+30, s)-Nets in Base 9

(56, 56+30, 448)-Net over F₉ — Constructive and digital

Digital (56, 86, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 43, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(56, 56+30, 1000)-Net over F₉ — Digital

Digital (56, 86, 1000)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+30, 237492)-Net in Base 9 — Upper bound on s

There is no (56, 86, 237493)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11610 631185 036104 713842 806378 007397 869142 250245 078449 140599 587598 887789 528169 726617 > 9⁸⁶ [i]