MinT - Best Known (69, 104, s)-Nets in Base 9

Best Known (69, 104, s)-Nets in Base 9

(69, 104, 740)-Net over F₉ — Constructive and digital

Digital (69, 104, 740)-net over F₉, using

2 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, 104, 1421)-Net over F₉ — Digital

Digital (69, 104, 1421)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 104, 542542)-Net in Base 9 — Upper bound on s

There is no (69, 104, 542543)-net in base 9, because

1 times m-reduction [i] would yield (69, 103, 542543)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 193 633207 984200 928081 188733 180440 770801 499462 090617 760419 991852 159686 828485 495126 163925 814572 487161 > 9¹⁰³ [i]