MinT - Best Known (69, 100, s)-Nets in Base 9

Best Known (69, 100, s)-Nets in Base 9

(69, 100, 740)-Net over F₉ — Constructive and digital

Digital (69, 100, 740)-net over F₉, using

6 times m-reduction [i] based on digital (69, 106, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 53, 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]

(69, 100, 2298)-Net over F₉ — Digital

Digital (69, 100, 2298)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 100, 1594684)-Net in Base 9 — Upper bound on s

There is no (69, 100, 1594685)-net in base 9, because

1 times m-reduction [i] would yield (69, 99, 1594685)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29512 777671 722734 685216 579629 360484 153105 113449 576660 969029 659018 939887 540990 237734 924363 885913 > 9⁹⁹ [i]