Howell designs fit neatly into this framework. Recently, Chee, Kiah, Zhang and Zhang [@CKZZ] noted that generalized packing designs are equivalent to [*multiply constant-weight codes*]{}, introduced in [@Chee2], which themselves generalize doubly constant-weight codes as discussed in Section \[PA-code\].

Suppose that $v,k,t,\lambda,m$ are integers where $v \geq k \geq t \geq 1$, $\lambda \geq 1$ and $m\geq 1$. Let ${\mathbf{v}}= (v_1,v_2,\ldots,v_m)$ and ${\mathbf{k}}=(k_1,k_2,\ldots,k_m)$ be $m$-tuples of positive integers with sum $v$ and $k$ respectively, where $k_i\leq v_i$ for all $i$, and let ${\mathbf{X}}= (X_1,X_2,\ldots,X_m)$ be an $m$-tuple of pairwise disjoint sets, where $|X_i|=v_i$. We say that an $m$-tuple of [*non-negative*]{} integers ${\mathbf{t}}=(t_1,t_2,\ldots,t_m)$ is [*admissible*]{} if $t_i\leq k_i$ for all $i$ and the entries $t_i$ sum to $t$. Now we define a [*$t$-$({\mathbf{v}},{\mathbf{k}},\lambda)$ generalized packing design*]{} to be a collection $\mathcal{P}$ of $m$-tuples of sets $(B_1,B_2,\ldots,B_m)$, where $B_i\subseteq X_i$ and $|B_i|=k_i$ for all $i$, with the property that for any admissible ${\mathbf{t}}$, any $m$-tuple of sets $(T_1,T_2,\ldots,T_m)$ (where $T_i\subseteq X_i$ and $|T_i|=t_i$ for all $i$) is contained in at most $\lambda$ members of $\mathcal{P}$. We say a generalized packing is [*optimal*]{} if it contains the largest possible number of blocks. (See [@packings] for further details, and for numerous examples.)

The connection 