New Constructions of Near-Complete External Difference Families Over Galois Rings

External difference families (EDFs for short) are a type of block designs that each nonidentity element arises a fixed number of times as a difference between elements in distinct blocks. An EDF with the property that the union of its blocks covers the nonidentity elements exactly once is called a near-complete EDF. In this letter, we obtain some near-complete EDFs from disjoint difference families and difference unit sets over Galois rings, and explicitly determine their parameters. The obtained EDFs cover some earlier EDFs as special cases. Furthermore, we confirmed the conjecture in Davis et al. (Des. Codes Cryptogr. 87(11): 415-424, 2017).