Time-hopping patterns can be constructed from simple difference sets. By studying such constructions, we prove that whenever n 2, n, n 1, or n + 1 is a prime power, then we can construct timehopping patterns that have n terms, and are of length less than n2. We show by computation that such patterns can have length less then n2 n’ for all n 5 150. We also show that time-hopping patterns of n te...