MinT - Best Known (132−30, 132, s)-Nets in Base 5

Best Known (132−30, 132, s)-Nets in Base 5

(132−30, 132, 504)-Net over F₅ — Constructive and digital

Digital (102, 132, 504)-net over F₅, using

t-expansion [i] based on digital (101, 132, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (35, 50, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 25, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
        the Hermitian function field over F₂₅ [i]
  2. digital (51, 82, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 41, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(132−30, 132, 4446)-Net over F₅ — Digital

Digital (102, 132, 4446)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−30, 132, 2273215)-Net in Base 5 — Upper bound on s

There is no (102, 132, 2273216)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 671438 610791 798718 474867 002136 806802 345956 439912 706970 596156 325337 652730 193372 189963 403009 > 5¹³² [i]