MinT - Best Known (124−77, 124, s)-Nets in Base 9

Best Known (124−77, 124, s)-Nets in Base 9

(124−77, 124, 81)-Net over F₉ — Constructive and digital

Digital (47, 124, 81)-net over F₉, using

t-expansion [i] based on digital (32, 124, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(124−77, 124, 162)-Net over F₉ — Digital

Digital (47, 124, 162)-net over F₉, using

t-expansion [i] based on digital (46, 124, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(124−77, 124, 2280)-Net in Base 9 — Upper bound on s

There is no (47, 124, 2281)-net in base 9, because

1 times m-reduction [i] would yield (47, 123, 2281)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2368 816915 943570 019546 087245 145322 917050 472207 756168 930905 161304 657572 653016 317647 903326 237410 192773 537497 170548 161905 > 9¹²³ [i]