MinT - Best Known (191−112, 191, s)-Nets in Base 4

Best Known (191−112, 191, s)-Nets in Base 4

(191−112, 191, 104)-Net over F₄ — Constructive and digital

Digital (79, 191, 104)-net over F₄, using

t-expansion [i] based on digital (73, 191, 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]

(191−112, 191, 112)-Net over F₄ — Digital

Digital (79, 191, 112)-net over F₄, using

t-expansion [i] based on digital (73, 191, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(191−112, 191, 773)-Net in Base 4 — Upper bound on s

There is no (79, 191, 774)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 393945 862042 013900 222314 951082 245859 402076 459747 247149 162489 117270 880433 698661 687528 504326 579855 063812 208899 949728 > 4¹⁹¹ [i]