Partitioned difference families: the storm has not yet passed

TL;DR

This paper critiques recent literature on zero difference balanced functions, emphasizing the importance of using partitioned difference families for clearer proofs and highlighting ongoing issues with trivial or incorrect results.

Contribution

It clarifies the role of partitioned difference families in the study of zero difference balanced functions and addresses persistent problems in the literature.

Findings

Recent papers often contain trivial or incorrect results.

Partitioned difference families provide a clearer framework.

The paper demonstrates how to handle a recent flawed publication.

Abstract

Two years ago, we alarmed the scientific community about the large number of bad papers in the literature on {\it zero difference balanced functions}, where direct proofs of seemingly new results are presented in an unnecessarily lengthy and convoluted way. Indeed, these results had been proved long before and very easily in terms of difference families. In spite of our report, papers of the same kind continue to proliferate. Regrettably, a further attempt to put the topic in order seems unavoidable. While some authors now follow our recommendation of using the terminology of {\it partitioned difference families}, their methods are still the same and their results are often trivial or even wrong. In this note, we show how a very recent paper of this type can be easily dealt with.