MinT - Best Known (97−35, 97, s)-Nets in Base 9

Best Known (97−35, 97, s)-Nets in Base 9

(97−35, 97, 448)-Net over F₉ — Constructive and digital

Digital (62, 97, 448)-net over F₉, using

1 times m-reduction [i] based on digital (62, 98, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 49, 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]

(97−35, 97, 910)-Net over F₉ — Digital

Digital (62, 97, 910)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−35, 97, 219532)-Net in Base 9 — Upper bound on s

There is no (62, 97, 219533)-net in base 9, because

1 times m-reduction [i] would yield (62, 96, 219533)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 485412 441343 344564 349797 776231 125452 770716 232188 939958 019336 301005 549938 944896 112808 319209 > 9⁹⁶ [i]