MinT - Best Known (69, 69+37, s)-Nets in Base 9

Best Known (69, 69+37, s)-Nets in Base 9

(69, 69+37, 740)-Net over F₉ — Constructive and digital

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, 69+37, 1170)-Net over F₉ — Digital

Digital (69, 106, 1170)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+37, 347889)-Net in Base 9 — Upper bound on s

There is no (69, 106, 347890)-net in base 9, because

1 times m-reduction [i] would yield (69, 105, 347890)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15684 667382 437206 385904 103800 377130 628554 517258 762873 882311 280189 212255 565015 531441 971480 379732 336865 > 9¹⁰⁵ [i]