MinT - Best Known (119−77, 119, s)-Nets in Base 9

Best Known (119−77, 119, s)-Nets in Base 9

(119−77, 119, 81)-Net over F₉ — Constructive and digital

Digital (42, 119, 81)-net over F₉, using

t-expansion [i] based on digital (32, 119, 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]

(119−77, 119, 140)-Net over F₉ — Digital

Digital (42, 119, 140)-net over F₉, using

t-expansion [i] based on digital (39, 119, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(119−77, 119, 1702)-Net in Base 9 — Upper bound on s

There is no (42, 119, 1703)-net in base 9, because

1 times m-reduction [i] would yield (42, 118, 1703)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40547 443502 883747 099395 205221 404536 028430 956444 620909 298905 333142 322543 613876 674119 111226 230413 900251 053599 830865 > 9¹¹⁸ [i]