need the concepts of trivial GHDs and subdesigns of GHDs. A $t$-${\mathrm{GHD}}_k(s,0;\lambda)$ is called [*trivial*]{}; that is, a trivial GHD is an empty $s \times s$ array. If a $t$-${\mathrm{GHD}}_k(s,v;\lambda)$, $\cG$, has a subarray $\cH$ which is itself a $t$-${\mathrm{GHD}}_k(s',v';\lambda')$ for some $s'\leq s$, $v' \leq v$ and $\lambda' \leq \lambda$ and whose point set is a pairwise hole, then we say that $\cH$ is a [*subdesign*]{} of $\cG$. In particular, if the subdesign $\cH$ is trivial, then we call $\cH$ an [*array hole*]{} in $\cG$, and say that $\cG$ has an array hole of size $s'$.

There is a third type of hole that may occur, a [*Latin hole*]{}, which is a set of elements $H \subseteq X$ and sets $R$, $C$ of rows and columns, respectively, such that each row in $R$ (resp. column in $C$) contains no points in $H$, but all points in $X \setminus H$. The concepts of array holes and Latin holes may coincide when there is an array hole in a Latin square, and each row and column intersecting the array hole misses the same subset $H$ of the point set. This is often referred to in the literature as a Latin square 