Finding high-quality mappings of Deep Neural Network (DNN) models onto tensor accelerators is critical for efficiency. State-of-the-art mapping exploration tools use remainderless (i.e., perfect) factorization to allocate hardware resources, through tiling the tensors, based on factors of tensor dimensions. This limits the size of the search space, (i.e., mapspace), but can lead to low resource utilization. We introduce a new mapspace, Ruby, that adds remainders (i.e., imperfect factorization) to expand the mapspace with high-quality mappings for user-defined architectures.