$(k,\lambda)$-GDD of type $g^u$, is a triple $(X,\cG, \cB)$, where $X$ is a set of $gu$ points, $\cG$ is a partition of $X$ into $u$ subsets, called [*groups*]{}, of size $g$, and $\cB$ is a collection of subsets, called [*blocks*]{}, of size $k$, with the properties that no pair of points in the same group appears together in a block, and each pair of points in different groups occurs in exactly one block. A $(k,1)$-GDD of type $n^k$ is called a [*transversal design*]{}, and denoted $\mathrm{T}(k,n)$. Note that a transversal design can be interpreted as a packing which misses the pairs contained in the groups. Alternatively, adding the groups as blocks, we may form from a transversal design a $\mathrm{PBD}(kn,\{k,n\})$. PBDs formed in this way will often be used as ingredients in the construction of GHDs in later sections.

A resolvable transversal design with block size $k$ and group size $n$ is denoted $\mathrm{RT}(k,n)$. It is well known that a set of $k$ MOLS of side $n$ is equivalent to an $\mathrm{RT}(k+1,n)$.

Subdesigns and holes
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The word [*hole*]{} is used with different meanings in different areas of design theory. For example, a hole in a BIBD refers to a 