The set of all possible intersection sizes between two simple triple systems \({TS}(v, \lambda_1)\) and \({TS}(v, \lambda_2)\) is denoted by \({Int}(v, \lambda_1, \lambda_2)\). In this paper, for \(6 \leq v \leq 14\), and for all feasible \(\lambda$’s, \({Int}(v, \lambda_1, \lambda_2)\) is determined.