Increasing coverings of rigid analytic varieties

Question

Let $K/\mathbb{Q}_p$ be complete and let $X/K$ be a rigid analytic variety. When does $X$ admit an "increasing" admissible covering by quasi-compact admissible (in the strong G-topology) open subsets? That is, there is a totally ordered set $(I,\preceq)$ and an admissible covering $\{U_i\}_{i \in \mathcal{I}}$ of $X$ in the strong G-topology, such that each $U_i$ is quasi-compact, and $U_i \subseteq U_j$ if $i \preceq j$ in $I$.