Let K be a set of positive integers and let G be an additive group. A $(G,K,1)$ difference packing is a set of subsets of G with sizes from K whose list of differences covers every element of G at most once. It is balanced if the number of blocks of size $k\in K$ does not depend on k. In this paper, we determine a balanced $({\mathbb{Z}}_{4u}\times {\mathbb{Z}}_{8v},\{4,5\},1)$ difference packing of the largest possible size whenever uv is odd. The corresponding optimal balanced $(4u,8v,\{4,5\},1)$ optical orthogonal signature pattern codes are also obtained.

中文翻译：

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在平衡 (Z4u×Z8v,{4,5},1) 差分包装上

设K是一组正整数，设G是一个可加组。一$(G,钾,1)$差异打包是G 的一组子集，其大小来自K，其差异列表最多覆盖G 的每个元素一次。如果大小的块数是平衡的$克\in 钾$不依赖于k。在本文中，我们确定了一个平衡的$({\mathbb{Z}}_{4你}\times {\mathbb{Z}}_{8v},\{4,5\},1)$当uv为奇数时，最大可能尺寸的差异包装。相应的最优平衡$(4你,8v,\{4,5\},1)$ 还获得了光学正交签名模式代码。