MinT - Best Known (87, 87+110, s)-Nets in Base 4

Best Known (87, 87+110, s)-Nets in Base 4

(87, 87+110, 104)-Net over F₄ — Constructive and digital

Digital (87, 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]

(87, 87+110, 129)-Net over F₄ — Digital

Digital (87, 197, 129)-net over F₄, using

t-expansion [i] based on digital (81, 197, 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+110, 975)-Net in Base 4 — Upper bound on s

There is no (87, 197, 976)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42130 976407 287094 053365 293146 522817 120956 389714 888689 424890 213491 343871 738688 406200 816974 905291 963003 248811 405950 745324 > 4¹⁹⁷ [i]