MinT - Best Known (69−55, 69, s)-Nets in Base 9

Best Known (69−55, 69, s)-Nets in Base 9

(69−55, 69, 64)-Net over F₉ — Constructive and digital

Digital (14, 69, 64)-net over F₉, using

t-expansion [i] based on digital (13, 69, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(69−55, 69, 329)-Net in Base 9 — Upper bound on s

There is no (14, 69, 330)-net in base 9, because

1 times m-reduction [i] would yield (14, 68, 330)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 80639 253412 801459 333522 738931 007359 965244 413089 902350 690424 856753 > 9⁶⁸ [i]