MinT - Best Known (131−52, 131, s)-Nets in Base 9

Best Known (131−52, 131, s)-Nets in Base 9

(131−52, 131, 448)-Net over F₉ — Constructive and digital

Digital (79, 131, 448)-net over F₉, using

1 times m-reduction [i] based on digital (79, 132, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 66, 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]

(131−52, 131, 711)-Net over F₉ — Digital

Digital (79, 131, 711)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−52, 131, 84729)-Net in Base 9 — Upper bound on s

There is no (79, 131, 84730)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101341 338295 856687 181182 730697 311080 605064 502431 278679 700908 153124 759589 071569 551412 982113 230225 549965 788165 125714 421092 675041 > 9¹³¹ [i]