MinT - Best Known (107−53, 107, s)-Nets in Base 9

Best Known (107−53, 107, s)-Nets in Base 9

(107−53, 107, 164)-Net over F₉ — Constructive and digital

Digital (54, 107, 164)-net over F₉, using

1 times m-reduction [i] based on digital (54, 108, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 54, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(107−53, 107, 218)-Net over F₉ — Digital

Digital (54, 107, 218)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−53, 107, 10230)-Net in Base 9 — Upper bound on s

There is no (54, 107, 10231)-net in base 9, because

1 times m-reduction [i] would yield (54, 106, 10231)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141238 257575 585474 452379 579564 974735 096811 376223 745528 151747 545640 034401 924807 394793 453402 850484 807089 > 9¹⁰⁶ [i]