MinT - Best Known (119−99, 119, s)-Nets in Base 9

Best Known (119−99, 119, s)-Nets in Base 9

(119−99, 119, 74)-Net over F₉ — Constructive and digital

Digital (20, 119, 74)-net over F₉, using

t-expansion [i] based on digital (17, 119, 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]

(119−99, 119, 84)-Net over F₉ — Digital

Digital (20, 119, 84)-net over F₉, using

t-expansion [i] based on digital (19, 119, 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]

(119−99, 119, 444)-Net in Base 9 — Upper bound on s

There is no (20, 119, 445)-net in base 9, because

1 times m-reduction [i] would yield (20, 118, 445)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40405 571707 518887 371308 599244 708313 232057 675833 735485 073368 708834 182960 062982 353398 828757 689599 664793 564144 331625 > 9¹¹⁸ [i]