  A network can contain numerous spanning trees. If two spanning trees
$T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be
pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if every two
of them are pairwisely edge-disjoint, they are called completely
edge-independent spanning trees (CEISTs for short). CEISTs can facilitate many
network functionalities, and constructing CEISTs as maximally allowed as
possible in a given network is a worthy undertaking. In this paper, we
establish the maximal number of CEISTs in the locally twisted cube network, and
propose an algorithm to construct $\lfloor \frac{n}{2} \rfloor$ CEISTs in
$LTQ_n$, the $n$-dimensional locally twisted cube. The proposed algorithm has
been actually implemented, and we present the outputs. Network broadcasting in
the $LTQ_n$ was simulated using $\lfloor\frac{n}{2}\rfloor$ CEISTs, and the
performance compared with broadcasting using a single tree.
