  The existence of Large sets of Kirkman Triple Systems (LKTS) is an old
problem in combinatorics. Known results are very limited, and a lot of them are
based on the works of Denniston \cite{MR0349416, MR0369086, MR535159,
MR539718}. The only known recursive constructions are an tripling construction
by Denniston \cite{MR535159}and a product construction by Lei \cite{MR1931492},
both constructs an LKTS($uv$) on the basis of an LKTS($v$).
  In this paper, we describe an construction of LKTS$(q^n+2)$ from LKTS$(q+2)$,
where $q$ is a prime power of the form $6t+1$. We could construct previous
unknown LKTS($v$) by this result, the smallest among them have $v=171,345,363$.
