MinT - Best Known (84, 201, s)-Nets in Base 4

Best Known (84, 201, s)-Nets in Base 4

(84, 201, 104)-Net over F₄ — Constructive and digital

Digital (84, 201, 104)-net over F₄, using

t-expansion [i] based on digital (73, 201, 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]

(84, 201, 129)-Net over F₄ — Digital

Digital (84, 201, 129)-net over F₄, using

t-expansion [i] based on digital (81, 201, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(84, 201, 844)-Net in Base 4 — Upper bound on s

There is no (84, 201, 845)-net in base 4, because

1 times m-reduction [i] would yield (84, 200, 845)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 628021 353615 747598 944924 575167 106858 265939 845361 594082 385285 187774 130055 221515 941733 499975 776411 817823 601226 575243 259400 > 4²⁰⁰ [i]