MinT - Best Known (20, 51, s)-Nets in Base 9

Best Known (20, 51, s)-Nets in Base 9

(20, 51, 74)-Net over F₉ — Constructive and digital

Digital (20, 51, 74)-net over F₉, using

t-expansion [i] based on digital (17, 51, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(20, 51, 84)-Net over F₉ — Digital

Digital (20, 51, 84)-net over F₉, using

t-expansion [i] based on digital (19, 51, 84)-net over F₉, using
- net from sequence [i] based on digital (19, 83)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
    - Drinfeld modules of rank 1 [i]

(20, 51, 1208)-Net in Base 9 — Upper bound on s

There is no (20, 51, 1209)-net in base 9, because

1 times m-reduction [i] would yield (20, 50, 1209)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 517351 087975 561517 340638 097643 011960 599219 153913 > 9⁵⁰ [i]