A (v, k, t) packing of size b is a system of b subsets (blocks) of a v-element underlying set such that each block has k elements and every t-set is contained in at most one block. P(v, k, t) stands for the maximum possible b. A packing is called abundant if \(b> v\). We give new estimates for P(v, k, t) around the critical range, slightly improving the Johnson bound and asymptotically determine the minimum \(v=v_0(k,t)\) when abundant packings exist. For a graph G and a positive integer c, let \(\chi _\ell (G,c)\) be the minimum value of k such that one can properly color the vertices of G from any assignment of lists L(v) such that \(|L(v)|=k\) for all \(v\in V(G)\) and \(|L(u)\cap L(v)|\le c\) for all \(uv\in E(G)\). Kratochvíl, Tuza and Voigt in 1998 asked to determine \(\lim _{n\rightarrow \infty } \chi _\ell (K_n,c)/\sqrt{cn}\) (if it exists). Using our bound on \(v_0(k,t)\), we prove that the limit exists and equals 1. Given c, we find the exact value of \(\chi _\ell (K_n,c)\) for infinitely many n.

大小为b 的A ( v , k , t ) 打包是v元素基础集合的b个子集（块）的系统，使得每个块具有k 个元素，并且每个t集合最多包含在一个块中。 P ( v , k , t )代表最大可能的b 。如果\(b> v\) ，则称包装为丰富的。我们在临界范围附近给出了P ( v , k , t ) 的新估计，稍微改进了约翰逊界限，并渐近地确定了存在丰富堆积时的最小值\(v=v_0(k,t)\) 。对于图G和正整数c ，令\(\chi _\ell (G,c)\)为k的最小值，这样人们就可以根据列表L ( v ) 的任何分配正确地为G的顶点着色这样对于所有\(v\in V(G)\)和\(|L(u)\cap L(v)|\le c\)对于所有\ (|L(v)|=k\) (uv\in E(G)\) 。 Kratochvíl、Tuza 和 Voigt 在 1998 年要求确定\(\lim _{n\rightarrow \infty } \chi _\ell (K_n,c)/\sqrt{cn}\) （如果存在）。使用\(v_0(k,t)\)上的界限，我们证明极限存在并且等于 1。给定c ，我们找到无限的\(\chi _\ell (K_n,c)\)的精确值许多n .