MinT - Best Known (113−93, 113, s)-Nets in Base 9

Best Known (113−93, 113, s)-Nets in Base 9

(113−93, 113, 74)-Net over F₉ — Constructive and digital

Digital (20, 113, 74)-net over F₉, using

t-expansion [i] based on digital (17, 113, 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]

(113−93, 113, 84)-Net over F₉ — Digital

Digital (20, 113, 84)-net over F₉, using

t-expansion [i] based on digital (19, 113, 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]

(113−93, 113, 445)-Net in Base 9 — Upper bound on s

There is no (20, 113, 446)-net in base 9, because

1 times m-reduction [i] would yield (20, 112, 446)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75439 015993 808751 975790 203938 682208 892166 730531 239543 475901 430039 593971 935269 656044 491863 308300 918328 216545 > 9¹¹² [i]