This paper presents an efficient and scalable collision checking method for large multi-robot teams based on a quad-tree data structure. We introduce several key modifications to the original quad-tree including rules for handling collision checks near boundaries. In addition, we provide a thorough performance comparison against pairwise collision checking, bounding volume hierarchies (BVH), and other variations of quad-trees. The results indicate that our proposed approach significantly outperforms other baselines in terms of collision checking time for large number of robots. For a 200-robot test, our approach achieved a 2.8x speedup over BVH and an 11.8x speedup over pairwise, without missing any collisions. However, pairwise collision checking remains a reasonable approach for small numbers of robots due to the reduced setup time needed.