MinT - Best Known (87, 87+118, s)-Nets in Base 4

Best Known (87, 87+118, s)-Nets in Base 4

(87, 87+118, 104)-Net over F₄ — Constructive and digital

Digital (87, 205, 104)-net over F₄, using

t-expansion [i] based on digital (73, 205, 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]

(87, 87+118, 129)-Net over F₄ — Digital

Digital (87, 205, 129)-net over F₄, using

t-expansion [i] based on digital (81, 205, 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]

(87, 87+118, 892)-Net in Base 4 — Upper bound on s

There is no (87, 205, 893)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2770 561843 072417 885836 273013 559041 114381 950120 228360 656540 443729 528642 024575 201240 691140 154687 527471 056937 305175 828986 050948 > 4²⁰⁵ [i]