MinT - Best Known (74, 74+20, s)-Nets in Base 5

Best Known (74, 74+20, s)-Nets in Base 5

(74, 74+20, 400)-Net over F₅ — Constructive and digital

Digital (74, 94, 400)-net over F₅, using

4 times m-reduction [i] based on digital (74, 98, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 49, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(74, 74+20, 5701)-Net over F₅ — Digital

Digital (74, 94, 5701)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+20, 4209530)-Net in Base 5 — Upper bound on s

There is no (74, 94, 4209531)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 504871 927743 786175 294275 118745 916350 400429 758114 092230 433364 613465 > 5⁹⁴ [i]