MinT - Best Known (74, 104, s)-Nets in Base 5

Best Known (74, 104, s)-Nets in Base 5

(74, 104, 296)-Net over F₅ — Constructive and digital

Digital (74, 104, 296)-net over F₅, using

6 times m-reduction [i] based on digital (74, 110, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 55, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(74, 104, 951)-Net over F₅ — Digital

Digital (74, 104, 951)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 104, 112682)-Net in Base 5 — Upper bound on s

There is no (74, 104, 112683)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 930576 461255 132733 221054 729277 441790 602818 296535 228567 995797 633227 740085 > 5¹⁰⁴ [i]