MinT - Best Known (51−37, 51, s)-Nets in Base 9

Best Known (51−37, 51, s)-Nets in Base 9

(51−37, 51, 64)-Net over F₉ — Constructive and digital

Digital (14, 51, 64)-net over F₉, using

t-expansion [i] based on digital (13, 51, 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]

(51−37, 51, 411)-Net in Base 9 — Upper bound on s

There is no (14, 51, 412)-net in base 9, because

1 times m-reduction [i] would yield (14, 50, 412)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 521516 591873 577416 755106 841469 177558 696082 571585 > 9⁵⁰ [i]