Ultrametric spaces bi-Lipschitz embeddable in ${\displaystyle {ℝ}^n}$

It is proved that if an ultrametric space can be bi-Lipschitz embedded in ${\displaystyle {ℝ}^n}$, then its Assouad dimension is less than n. Together with a result of Luukkainen and Movahedi-Lankarani, where the converse was shown, this gives a characterization in terms of Assouad dimension of the ultrametric spaces which are bi-Lipschitz embeddable in ${\displaystyle {ℝ}^n}$.