MinT - Best Known (97−33, 97, s)-Nets in Base 9

Best Known (97−33, 97, s)-Nets in Base 9

(97−33, 97, 448)-Net over F₉ — Constructive and digital

Digital (64, 97, 448)-net over F₉, using

5 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]

(97−33, 97, 1264)-Net over F₉ — Digital

Digital (64, 97, 1264)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−33, 97, 451746)-Net in Base 9 — Upper bound on s

There is no (64, 97, 451747)-net in base 9, because

1 times m-reduction [i] would yield (64, 96, 451747)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 484684 359169 995000 256259 543777 107958 219327 726790 373486 890050 614264 929149 491213 784779 236737 > 9⁹⁶ [i]