MinT - Best Known (64, 64+37, s)-Nets in Base 9

Best Known (64, 64+37, s)-Nets in Base 9

(64, 64+37, 448)-Net over F₉ — Constructive and digital

Digital (64, 101, 448)-net over F₉, using

1 times m-reduction [i] based on digital (64, 102, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 51, 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]

(64, 64+37, 867)-Net over F₉ — Digital

Digital (64, 101, 867)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+37, 188956)-Net in Base 9 — Upper bound on s

There is no (64, 101, 188957)-net in base 9, because

1 times m-reduction [i] would yield (64, 100, 188957)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 265617 811900 712215 368867 166842 332141 695389 414517 430914 303946 445096 368437 021126 964250 715577 028369 > 9¹⁰⁰ [i]