MinT - Best Known (19, 19+39, s)-Nets in Base 9

Best Known (19, 19+39, s)-Nets in Base 9

(19, 19+39, 74)-Net over F₉ — Constructive and digital

Digital (19, 58, 74)-net over F₉, using

t-expansion [i] based on digital (17, 58, 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]

(19, 19+39, 84)-Net over F₉ — Digital

Digital (19, 58, 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]

(19, 19+39, 711)-Net in Base 9 — Upper bound on s

There is no (19, 58, 712)-net in base 9, because

1 times m-reduction [i] would yield (19, 57, 712)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 517151 760742 503621 729682 890609 851906 266309 921121 264065 > 9⁵⁷ [i]