The spectrum of resolvable 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, which exists whenever n is odd. In an application to access-balancing in storage systems, certain Bose triple systems play a central role. A natural question arises: For which orders v does there exist a resolvable Bose triple system? Elementary counting establishes the necessary condition that v equivalent to 9 (mod 18). For specific Bose triple systems that optimize an access metric, we show that v equivalent to 9 (mod 18) is also sufficient.(c) 2023 Elsevier B.V. All rights reserved.