MinT - Best Known (90−42, 90, s)-Nets in Base 5

Best Known (90−42, 90, s)-Nets in Base 5

(90−42, 90, 104)-Net over F₅ — Constructive and digital

Digital (48, 90, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 45, 52)-net over F₂₅, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]

(90−42, 90, 121)-Net over F₅ — Digital

Digital (48, 90, 121)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−42, 90, 2132)-Net in Base 5 — Upper bound on s

There is no (48, 90, 2133)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 810 087221 958530 538930 712626 526908 401895 005641 033979 164082 496325 > 5⁹⁰ [i]