Further results on (v,4,1)(v,4,1)-perfect difference families

In this paper, it is shown that an ASP(2r+1,3)(2r+1,3) exists for 2≤r≤1002≤r≤100 and r≠4,5r≠4,5. The existence of a (v,4,1)(v,4,1)-PDF is investigated by taking advantage of the relationship between ASPs and perfect difference families (PDFs). It is proved that a (12t+1,4,1)(12t+1,4,1)-PDF exists for t≤100t≤100 and t≠2,3t≠2,3. Several recursive constructions for ASPs and PDFs are also presented. As a consequence, the existence results of an optimal (v,4,1)(v,4,1)-OOC is updated.