论文
应用数学学报(英文版).
2008, 24(2):
233-252.
In this paper, we first introduce a special structure that
allows us to construct a large set of resolvable Mendelsohn triple
systems of orders $2q+2$, or LRMTS$(2q+2)$, where $q=6t+5$ is a
prime power. Using a computer, we find examples of such structure
for $t\in T=\{0,1,2,3,4,6,7,8,9,14,16,18,20,22,24\}$. Furthermore,
by a method we introduced in [13], large set of resolvable directed
triple systems with the same orders are obtained too. Finally, by
the tripling construction and product construction for LRMTS and
LRDTS introduced in [2, 20, 21], and by the new results for
$LR$-design in [8], we obtain the existence for LRMTS$(v)$ and
$LRDTS(v)$, where $v=12(t+1)\prod\limits_{m_i\geq0}(2\cdot7^{m_i}+1)
\prod\limits_{n_i\geq0}(2\cdot13^{n_i}+1)$ and $t\in T$, which
provides more infinite family for LRMTS and LRDTS of even orders.