MinT - Best Known (112−93, 112, s)-Nets in Base 9

Best Known (112−93, 112, s)-Nets in Base 9

(112−93, 112, 74)-Net over F₉ — Constructive and digital

Digital (19, 112, 74)-net over F₉, using

t-expansion [i] based on digital (17, 112, 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]

(112−93, 112, 84)-Net over F₉ — Digital

Digital (19, 112, 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]

(112−93, 112, 423)-Net in Base 9 — Upper bound on s

There is no (19, 112, 424)-net in base 9, because

1 times m-reduction [i] would yield (19, 111, 424)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8446 358513 090823 934818 865941 965047 342369 345560 223134 531483 893336 265643 338695 429418 946683 521508 627778 609281 > 9¹¹¹ [i]