MinT - Best Known (72−28, 72, s)-Nets in Base 5

Best Known (72−28, 72, s)-Nets in Base 5

(72−28, 72, 132)-Net over F₅ — Constructive and digital

Digital (44, 72, 132)-net over F₅, using

8 times m-reduction [i] based on digital (44, 80, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 40, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(72−28, 72, 199)-Net over F₅ — Digital

Digital (44, 72, 199)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−28, 72, 5934)-Net in Base 5 — Upper bound on s

There is no (44, 72, 5935)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 212 105176 083196 230280 222077 621011 415194 103868 341705 > 5⁷² [i]