MinT - Best Known (60, 125, s)-Nets in Base 9

Best Known (60, 125, s)-Nets in Base 9

(60, 125, 128)-Net over F₉ — Constructive and digital

Digital (60, 125, 128)-net over F₉, using

3 times m-reduction [i] based on digital (60, 128, 128)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 47, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
        a function field by GarcÃa and Quoos [i]
  2. digital (13, 81, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉ (see above)

(60, 125, 201)-Net over F₉ — Digital

Digital (60, 125, 201)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 125, 7950)-Net in Base 9 — Upper bound on s

There is no (60, 125, 7951)-net in base 9, because

1 times m-reduction [i] would yield (60, 124, 7951)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21194 413023 956389 259827 222409 900826 474994 924792 684957 790411 487876 848808 164737 824721 490086 688141 129241 159331 946313 756417 > 9¹²⁴ [i]