mBED has time complexity $O(n \lg n)$, claimed by Clustal Omega paper, why?
Turns out that I was dumb: I misread.
The Clustal Omega paper (in the supplementary materials) chose $t = \log N$, which I think originates from this claim from this part of the Linial et al. paper:

In random polynomial time $X$ may be embedded in $l_{2}^{O(\log n)}$ with distortion $\leq(1+\epsilon) \cdot c_{2}(X)$ (for any $\epsilon&gt;0)$

Several questions still remain though:

The newest implementation of Clustal Omega (that I downloaded) has source code that instead chooses $t = (\log N)^2$, why changed?
The original mBED paper chooses $t = (\log N)^2$, but it was not justified on how they chose this number instead of $\log N$