MinT - Best Known (129−53, 129, s)-Nets in Base 9

Best Known (129−53, 129, s)-Nets in Base 9

(129−53, 129, 344)-Net over F₉ — Constructive and digital

Digital (76, 129, 344)-net over F₉, using

9 times m-reduction [i] based on digital (76, 138, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 69, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(129−53, 129, 590)-Net over F₉ — Digital

Digital (76, 129, 590)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−53, 129, 65751)-Net in Base 9 — Upper bound on s

There is no (76, 129, 65752)-net in base 9, because

1 times m-reduction [i] would yield (76, 128, 65752)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 139 013838 375424 537488 881392 944473 720818 391015 324822 649285 578680 591651 089291 771621 355034 699886 643519 663322 224393 238401 949313 > 9¹²⁸ [i]