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This is a follow-up to my previous question: Generators of $GL_n(\Bbb Z)$ and $GL_n(\Bbb Z_p)$

Let $\mathcal{O}_K$ be the ring of integers in a characteristic zero non-archimedean local field $K$.

What is the minimal number of topological generators of $SL_n(\mathcal{O}_K)$?

In particular, is this number bounded independent of $n$? Independent of $K$? I'd also be interested in any information when $K$ is a number field, as well.

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