Resolutions for an infinite family of Bose triple systems (Q6616801)

In an application to access-balancing in storage systems, one desires a point labelling of a Steiner triple system that maximizes a certain metric, namely the MinSum metric. It is known that the so-called Bose-averaging triple systems on \(v \equiv 3 \bmod 6\) points can be labelled to achieve this maximum. See [\textit{H. Dau} and \textit{O. Milenkovic}, SIAM J. Discrete Math. 32, No. 3, 1644--1671 (2018; Zbl 1391.05053)]. The precise definitions are too technical to be given in this review.\N\NIn this context, it is interesting to study the problem of the resolvability of Bose-averaging triple systems. The main result of the paper under review is the construction of a resolution of the Bose-averaging triple system of order \(3n\) whenever \(n = 3p\) for some prime \(p \geq 5\).\N\NSubsequently, the authors prove the following general result: Every resolvable Bose triple system of order \(v\) has \(v \equiv 9 \bmod 18\), and the Bose-averaging triple system of this order is actually resolvable. See [\textit{D. Lusi} and \textit{C. J. Colbourn}, Discrete Math. 346, No. 7, Article ID 113396, 9 p. (2023; Zbl 1514.05025)].\N\NFor the entire collection see [Zbl 1540.05004].