MinT - Best Known (80, 189, s)-Nets in Base 4

Best Known (80, 189, s)-Nets in Base 4

(80, 189, 104)-Net over F₄ — Constructive and digital

Digital (80, 189, 104)-net over F₄, using

t-expansion [i] based on digital (73, 189, 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, 189, 112)-Net over F₄ — Digital

Digital (80, 189, 112)-net over F₄, using

t-expansion [i] based on digital (73, 189, 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, 189, 828)-Net in Base 4 — Upper bound on s

There is no (80, 189, 829)-net in base 4, because

1 times m-reduction [i] would yield (80, 188, 829)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 160964 272948 976633 837103 262539 309504 392972 531200 603594 245057 652868 536344 251652 777097 748174 332251 392627 826035 855140 > 4¹⁸⁸ [i]