MinT - Best Known (53, 53+48, s)-Nets in Base 9

Best Known (53, 53+48, s)-Nets in Base 9

(53, 53+48, 232)-Net over F₉ — Constructive and digital

Digital (53, 101, 232)-net over F₉, using

1 times m-reduction [i] based on digital (53, 102, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 51, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(53, 53+48, 247)-Net over F₉ — Digital

Digital (53, 101, 247)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+48, 12692)-Net in Base 9 — Upper bound on s

There is no (53, 101, 12693)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 392725 118500 942954 179877 512998 004979 316864 516257 713315 331430 547922 627558 030751 710074 720671 556289 > 9¹⁰¹ [i]