MinT - Best Known (80, 80+138, s)-Nets in Base 4

Best Known (80, 80+138, s)-Nets in Base 4

(80, 80+138, 104)-Net over F₄ — Constructive and digital

Digital (80, 218, 104)-net over F₄, using

t-expansion [i] based on digital (73, 218, 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]

(80, 80+138, 112)-Net over F₄ — Digital

Digital (80, 218, 112)-net over F₄, using

t-expansion [i] based on digital (73, 218, 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]

(80, 80+138, 650)-Net in Base 4 — Upper bound on s

There is no (80, 218, 651)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 185763 480800 886275 056012 051433 930198 604060 109796 628892 321595 554995 527799 021367 862658 222490 348610 874903 303981 393669 525174 815681 605960 > 4²¹⁸ [i]