Let $p$ be a prime, $L$ be a finite, totally ramified-extension of $Q_p,$ and $U$ be the group of principal units in the ring of integers of $L.$ Then $U$ is a finitely generated $\mathbb{Z}_p$-module under exponentiation. I'm looking for an explicit set of generators for $U$ under this action; is there a resource where I can find this information?

Let $p$ be a prime, $L$ be a finite, totally ramified-extension of $Q_p,$ and $U$ be the group of principal units in the ring of integers of $L.$ Then $U$ is a finitely generated $\mathbb{Z}_p$-module under exponentiation. I'm looking for an explicit set of generators for $U$ under this action; is there a resource where I can find this information?

Thanks Robin but am I afraid I need more control on the set of generators. In particular, I'm interested if G is a set of generators of the value m = max {$v_L(g-1):g\in G$}