An exclusive set system is a family of subsets of a universe with the property that every large subset may be written as the union of subsets from the family. We obtain new upper bounds on the size of such families, showing that in a universe of n elements, there is a system of 48k3 (nk)r/k In subsets with the property that every subset of the universe of size n -- r can be written as the union of k subsets in the system. Such sets systems form the combinatorial foundation of many broadcast encryption schemes.
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机译：独家集系统是一个宇宙的子集家族，其中每个大小的子集可能被写为来自家庭的子集合。我们在这些家庭的大小上获得了新的上限，表明在N个元素的宇宙中，有一个48 k 3 （ nk ） r / k 在子集中，其中包含大小的宇宙的每个子集 n - r 可以写作系统中 k 子集的联盟。这样的集合系统形成了许多广播加密方案的组合基础。
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