L. Ji

A Steiner system $S(t,k,v)$ is called $i$-resolvable, $0< i< t$, if its block set can be partitioned into $S(i,k,v)$. A $1$-resolvable $S(2,3,v)$ is also called a {\it Kirkman triple system} of order $v$ and shortly denoted by KTS$(v)$.
Two KTS$(v)$ $(X,{\cal A})$ and $(X,{\cal B})$ are called {\em disjoint} if ${\cal A}\cap {\cal B}=\emptyset$. A set of more than two KTS$(v)$ is called disjoint if each pair of them is disjoint. A set of $v-2$ disjoint KTS$(v)$ is called a {\it large set of disjoint Kirkman triple systems} of order $v$ and briefly denoted by LKTS$(v)$.
In this paper, we shall utilize $2$-resolvable $S(3,4,v)$ (SQS$(v)$) to study LKTS. For this purpose, we also introduce a resolvable partitionable candelabra system and a resolvable partitionable group divisible design, and use them to give a construction of LKTS$(3v-3)$ from a 2-resolvable SQS$(v)$. With the known results on 2-resolvable SQS$(v)$, we obtain the following new LKTSs.
Theorem. There is an LKTS$(v)$ for $v=3\cdot 4^n-3$, or $v=6\cdot p^n+3$ with $p\in \{7,31,127\}$, for any positive integer $n$.