MinT - Best Known (197−114, 197, s)-Nets in Base 4

Best Known (197−114, 197, s)-Nets in Base 4

(197−114, 197, 104)-Net over F₄ — Constructive and digital

Digital (83, 197, 104)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(197−114, 197, 129)-Net over F₄ — Digital

Digital (83, 197, 129)-net over F₄, using

t-expansion [i] based on digital (81, 197, 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]

(197−114, 197, 840)-Net in Base 4 — Upper bound on s

There is no (83, 197, 841)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41867 784963 630233 269266 629391 575841 150017 748243 840275 971394 432301 311831 902119 381697 325932 800005 502502 042646 139937 502800 > 4¹⁹⁷ [i]