MinT - Best Known (122−47, 122, s)-Nets in Base 9

Best Known (122−47, 122, s)-Nets in Base 9

(122−47, 122, 448)-Net over F₉ — Constructive and digital

Digital (75, 122, 448)-net over F₉, using

2 times m-reduction [i] based on digital (75, 124, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 62, 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]

(122−47, 122, 787)-Net over F₉ — Digital

Digital (75, 122, 787)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−47, 122, 123441)-Net in Base 9 — Upper bound on s

There is no (75, 122, 123442)-net in base 9, because

1 times m-reduction [i] would yield (75, 121, 123442)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29 063355 780053 517092 506725 271715 391924 697509 711877 118080 082939 565224 136479 076638 968273 605305 209740 133706 777499 467697 > 9¹²¹ [i]