MinT - Best Known (89, 89+57, s)-Nets in Base 9

Best Known (89, 89+57, s)-Nets in Base 9

(89, 89+57, 740)-Net over F₉ — Constructive and digital

Digital (89, 146, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 73, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(89, 89+57, 845)-Net over F₉ — Digital

Digital (89, 146, 845)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+57, 123443)-Net in Base 9 — Upper bound on s

There is no (89, 146, 123444)-net in base 9, because

1 times m-reduction [i] would yield (89, 145, 123444)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 318530 822307 198219 487797 111700 771775 304831 593596 053851 106000 406877 869809 848679 753875 753035 369439 521269 856238 093062 177655 110823 910947 211905 > 9¹⁴⁵ [i]