MinT - Best Known (118−78, 118, s)-Nets in Base 9

Best Known (118−78, 118, s)-Nets in Base 9

(118−78, 118, 81)-Net over F₉ — Constructive and digital

Digital (40, 118, 81)-net over F₉, using

t-expansion [i] based on digital (32, 118, 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]

(118−78, 118, 140)-Net over F₉ — Digital

Digital (40, 118, 140)-net over F₉, using

t-expansion [i] based on digital (39, 118, 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]

(118−78, 118, 1460)-Net in Base 9 — Upper bound on s

There is no (40, 118, 1461)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40322 865266 677706 220579 249507 292385 312446 568403 660954 525020 089542 208970 853338 093331 980830 176017 210981 409725 459289 > 9¹¹⁸ [i]