  A $k$-tuple total dominating set ($k$TDS) of a graph $G$ is a set $S$ of
vertices in which every vertex in $G$ is adjacent to at least $k$ vertices in
$S$. The minimum size of a $k$TDS is called the $k$-tuple total dominating
number and it is denoted by $\gamma_{\times k,t}(G)$. We give a constructive
proof of a general formula for $\gamma_{\times 3, t}(K_n \Box K_m)$.
