MinT - Best Known (94−29, 94, s)-Nets in Base 9

Best Known (94−29, 94, s)-Nets in Base 9

(94−29, 94, 740)-Net over F₉ — Constructive and digital

Digital (65, 94, 740)-net over F₉, using

4 times m-reduction [i] based on digital (65, 98, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 49, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(94−29, 94, 2270)-Net over F₉ — Digital

Digital (65, 94, 2270)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−29, 94, 1649157)-Net in Base 9 — Upper bound on s

There is no (65, 94, 1649158)-net in base 9, because

1 times m-reduction [i] would yield (65, 93, 1649158)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55533 315621 244726 257257 782583 416607 347832 498830 103178 665499 681890 842713 960253 157648 703585 > 9⁹³ [i]