MinT - Best Known (56−32, 56, s)-Nets in Base 9

Best Known (56−32, 56, s)-Nets in Base 9

(56−32, 56, 78)-Net over F₉ — Constructive and digital

Digital (24, 56, 78)-net over F₉, using

t-expansion [i] based on digital (22, 56, 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]

(56−32, 56, 92)-Net over F₉ — Digital

Digital (24, 56, 92)-net over F₉, using

t-expansion [i] based on digital (23, 56, 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]

(56−32, 56, 1849)-Net in Base 9 — Upper bound on s

There is no (24, 56, 1850)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 274855 202767 692117 238266 196135 101343 547944 559224 282881 > 9⁵⁶ [i]