Existence of optimal restricted strong partially balanced designs

Abstract

Restricted strong partially balanced t-designs were first formulated by Pei, Li, Wang and Safavi-Naini in recent investigation of authentication codes with arbitration. This article investigates the existence of optimal restricted strong partially balanced 2-design ORSPBD(v, 2 × k, 1) for k=2 and 3, and shows that there exists an ORSPBD(v, 2 × k, 1) for any v ≥ 2k except (k,v) = (3,10).