MinT - Best Known (66, 66+63, s)-Nets in Base 9

Best Known (66, 66+63, s)-Nets in Base 9

(66, 66+63, 200)-Net over F₉ — Constructive and digital

Digital (66, 129, 200)-net over F₉, using

1 times m-reduction [i] based on digital (66, 130, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 65, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(66, 66+63, 270)-Net over F₉ — Digital

Digital (66, 129, 270)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+63, 13503)-Net in Base 9 — Upper bound on s

There is no (66, 129, 13504)-net in base 9, because

1 times m-reduction [i] would yield (66, 128, 13504)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 139 283642 285039 732839 623079 801322 914532 599438 965770 924492 024973 312404 519221 564140 519349 605442 905875 593010 553257 585552 241153 > 9¹²⁸ [i]