MinT - Best Known (70, 95, s)-Nets in Base 5

Best Known (70, 95, s)-Nets in Base 5

(70, 95, 304)-Net over F₅ — Constructive and digital

Digital (70, 95, 304)-net over F₅, using

5¹ times duplication [i] based on digital (69, 94, 304)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (12, 24, 52)-net over F₅, using
    - trace code for nets [i] based on digital (0, 12, 26)-net over F₂₅, using
      - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
  2. digital (45, 70, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 35, 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]

(70, 95, 1444)-Net over F₅ — Digital

Digital (70, 95, 1444)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 95, 394963)-Net in Base 5 — Upper bound on s

There is no (70, 95, 394964)-net in base 5, because

1 times m-reduction [i] would yield (70, 94, 394964)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 504876 594247 032642 425201 867198 164569 166821 507131 119958 711065 484033 > 5⁹⁴ [i]