  Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum
possible length q+1. The classification of deep holes --received words with
maximum possible error distance-- for PRS codes is an important and difficult
problem. In this paper, we use algebraic methods to explicitly construct three
classes of deep holes for PRS codes. We show that these three classes
completely classify all deep holes of PRS codes with redundancy at most four.
Previously, the deep hole classification was only known for PRS codes with
redundancy at most three in work arXiv:1612.05447
