Let \((G,+)\) be a finite group, and let W be a set of integers greater than 1. A (G, W, 1)-difference packing is a family of subsets of G, each of size from W, whose list of differences covers every element of G at most once. Such a packing is balanced if it contains the same number of blocks of size w for each \(w\in W\) . In this paper, we focus on constructing optimal balanced \((\mathbb {Z}_{m}\times \mathbb {Z}_{n},\{4,5\},1)\) -difference packings for all even integers m, n satisfying \(mn\equiv 0\pmod {32}\) . As an application, we establish the corresponding family of optimal balanced \((m,n,\{4,5\},1)\) -optical orthogonal signature pattern codes. A new recursive construction based on balanced \(\{m,n\}\) -cyclic group divisible designs plays a key role.
