MinT - Best Known (54−30, 54, s)-Nets in Base 9

Best Known (54−30, 54, s)-Nets in Base 9

(54−30, 54, 78)-Net over F₉ — Constructive and digital

Digital (24, 54, 78)-net over F₉, using

t-expansion [i] based on digital (22, 54, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(54−30, 54, 92)-Net over F₉ — Digital

Digital (24, 54, 92)-net over F₉, using

t-expansion [i] based on digital (23, 54, 92)-net over F₉, using
- net from sequence [i] based on digital (23, 91)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 23 and N(F) ≥ 92, using
    - Drinfeld modules of rank 1 [i]

(54−30, 54, 2178)-Net in Base 9 — Upper bound on s

There is no (24, 54, 2179)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3389 651375 308081 423523 799258 630415 633439 063128 393449 > 9⁵⁴ [i]