MinT - Best Known (74, 74+81, s)-Nets in Base 4

Best Known (74, 74+81, s)-Nets in Base 4

(74, 74+81, 104)-Net over F₄ — Constructive and digital

Digital (74, 155, 104)-net over F₄, using

t-expansion [i] based on digital (73, 155, 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]

(74, 74+81, 112)-Net over F₄ — Digital

Digital (74, 155, 112)-net over F₄, using

t-expansion [i] based on digital (73, 155, 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]

(74, 74+81, 1060)-Net in Base 4 — Upper bound on s

There is no (74, 155, 1061)-net in base 4, because

1 times m-reduction [i] would yield (74, 154, 1061)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 531 302785 421563 863079 378057 945175 764281 504101 601255 880155 829162 265750 354720 499166 998924 795520 > 4¹⁵⁴ [i]