MinT - Best Known (88−29, 88, s)-Nets in Base 9

Best Known (88−29, 88, s)-Nets in Base 9

(88−29, 88, 448)-Net over F₉ — Constructive and digital

Digital (59, 88, 448)-net over F₉, using

4 times m-reduction [i] based on digital (59, 92, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 46, 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]

(88−29, 88, 1423)-Net over F₉ — Digital

Digital (59, 88, 1423)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−29, 88, 643128)-Net in Base 9 — Upper bound on s

There is no (59, 88, 643129)-net in base 9, because

1 times m-reduction [i] would yield (59, 87, 643129)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104496 745739 014051 846624 854067 771949 495626 740088 812471 450724 933996 246745 752697 513649 > 9⁸⁷ [i]