MinT - Best Known (101, 101+159, s)-Nets in Base 4

Best Known (101, 101+159, s)-Nets in Base 4

(101, 101+159, 104)-Net over F₄ — Constructive and digital

Digital (101, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(101, 101+159, 144)-Net over F₄ — Digital

Digital (101, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(101, 101+159, 885)-Net in Base 4 — Upper bound on s

There is no (101, 260, 886)-net in base 4, because

1 times m-reduction [i] would yield (101, 259, 886)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 932172 657006 054945 508269 707980 096839 050922 494815 824610 956698 975023 938416 826626 062547 014292 750890 978313 025907 156110 881446 927313 979006 961623 255080 351123 176744 > 4²⁵⁹ [i]