MinT - Best Known (85, 85+110, s)-Nets in Base 4

Best Known (85, 85+110, s)-Nets in Base 4

(85, 85+110, 104)-Net over F₄ — Constructive and digital

Digital (85, 195, 104)-net over F₄, using

t-expansion [i] based on digital (73, 195, 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]

(85, 85+110, 129)-Net over F₄ — Digital

Digital (85, 195, 129)-net over F₄, using

t-expansion [i] based on digital (81, 195, 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]

(85, 85+110, 925)-Net in Base 4 — Upper bound on s

There is no (85, 195, 926)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2653 425231 333012 210337 269864 505775 975236 421845 524298 790321 479773 833831 602557 607694 581735 159855 275884 995820 116061 383792 > 4¹⁹⁵ [i]