MinT - Best Known (80, 80+117, s)-Nets in Base 4

Best Known (80, 80+117, s)-Nets in Base 4

(80, 80+117, 104)-Net over F₄ — Constructive and digital

Digital (80, 197, 104)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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+117, 112)-Net over F₄ — Digital

Digital (80, 197, 112)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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+117, 763)-Net in Base 4 — Upper bound on s

There is no (80, 197, 764)-net in base 4, because

1 times m-reduction [i] would yield (80, 196, 764)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10434 309742 663267 592056 376259 896703 107403 204764 539582 265494 860922 337849 572019 769207 225666 639417 504002 623671 096810 843085 > 4¹⁹⁶ [i]