Special overlarge sets of Kirkman triple systems

A Steiner quadruple system of order \(v+1\) $v+1$ with resolvable derived designs (every derived Steiner triple system of order v at a point is resolvable), abbreviated as RDSQS \((v+1)\) $(v+1)$ , has been used to construct a large set of Kirkman triple systems of order 3v. In this paper, an RDSQS \((v+1)\) $(v+1)$ is reduced to an overlarge set of Kirkman triple systems of order v with an additional property (OLKTS \(^+(v)\) ${}^{+}(v)$ ), which plays the same role in constructing an LKTS(3v) as an RDSQS \((v+1)\) $(v+1)$ . Some recursive constructions of OLKTS \(^+\) ${}^{+}$ s are also established. As a result, some infinite classes of OLKTS \(^+\) ${}^{+}$ s and LKTSs are obtained.