MinT - Best Known (90, 90+44, s)-Nets in Base 5

Best Known (90, 90+44, s)-Nets in Base 5

(90, 90+44, 296)-Net over F₅ — Constructive and digital

Digital (90, 134, 296)-net over F₅, using

8 times m-reduction [i] based on digital (90, 142, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 71, 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]

(90, 90+44, 648)-Net over F₅ — Digital

Digital (90, 134, 648)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+44, 40924)-Net in Base 5 — Upper bound on s

There is no (90, 134, 40925)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4592 387314 280053 066852 361891 716955 770457 164798 591249 265749 919688 355915 234074 211129 053492 201801 > 5¹³⁴ [i]