MinT - Best Known (195−112, 195, s)-Nets in Base 4

Best Known (195−112, 195, s)-Nets in Base 4

(195−112, 195, 104)-Net over F₄ — Constructive and digital

Digital (83, 195, 104)-net over F₄, using

t-expansion [i] based on digital (73, 195, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(195−112, 195, 129)-Net over F₄ — Digital

Digital (83, 195, 129)-net over F₄, using

t-expansion [i] based on digital (81, 195, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(195−112, 195, 858)-Net in Base 4 — Upper bound on s

There is no (83, 195, 859)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2631 083899 598506 683935 709279 462868 855964 131781 137478 172399 032404 107197 367514 023320 562533 331861 298532 015652 093406 820026 > 4¹⁹⁵ [i]