MinT - Best Known (57−37, 57, s)-Nets in Base 9

Best Known (57−37, 57, s)-Nets in Base 9

(57−37, 57, 74)-Net over F₉ — Constructive and digital

Digital (20, 57, 74)-net over F₉, using

t-expansion [i] based on digital (17, 57, 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]

(57−37, 57, 84)-Net over F₉ — Digital

Digital (20, 57, 84)-net over F₉, using

t-expansion [i] based on digital (19, 57, 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]

(57−37, 57, 867)-Net in Base 9 — Upper bound on s

There is no (20, 57, 868)-net in base 9, because

1 times m-reduction [i] would yield (20, 56, 868)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 274474 742719 247286 518232 866536 375698 805326 019456 144065 > 9⁵⁶ [i]