  An edge labeling of a connected graph $G = (V, E)$ is said to be local
antimagic if there is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any
pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced
vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all the edges incident
to $x$. The local antimagic chromatic number of $G$, denoted by $\chi_{la}(G)$,
is the minimum number of distinct induced vertex labels over all local
antimagic labelings of $G$. In this paper, we give three ways to construct a
$(3m+2)\times (2k+1)$ matrix that meets certain properties for $m=1,3$ and
$k\ge 1$. Consequently, we obtained many (disconnected) graphs of size
$(3m+2)(2k+1)$ with local antimagic chromatic number 3.
