MinT - Best Known (131, 131+90, s)-Nets in Base 4

Best Known (131, 131+90, s)-Nets in Base 4

(131, 131+90, 134)-Net over F₄ — Constructive and digital

Digital (131, 221, 134)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (13, 58, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. digital (73, 163, 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]

(131, 131+90, 301)-Net over F₄ — Digital

Digital (131, 221, 301)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+90, 5282)-Net in Base 4 — Upper bound on s

There is no (131, 221, 5283)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 436874 077710 205887 105935 638131 182067 276145 370297 674567 099978 304701 154488 092939 231212 687676 302792 346028 567931 039978 391251 330066 262848 > 4²²¹ [i]