Resolutions for an Infinite Family of Bose Triple Systems

A classical construction of Bose produces a Steiner triple system of order 3n from a symmetric, idempotent latin square of order n whenever n is odd. In an application to access-balancing in storage systems, these Bose triple systems play a central role. A natural question arises: For which orders n does there exist a resolvable Bose triple system? In this paper, a resolution of the Bose-averaging triple system of order 3n is determined whenever \(n = 3p\) and \(p \ge 5\) is prime.