For positive integers $n\ge k\ge t$, a collection $\mathcal{B}$ of $k$‐subsets of an $n$‐set $X$ is called a $t$‐packing if every $t$‐subset of $X$ appears in at most one set in $\mathcal{B}$. In this paper, we investigate the existence of the maximum 3‐packings whenever $n$ is sufficiently larger than $k$. When $n\not\equiv 2\left(\mathrm{mod}k-2\right)$, the optimal value for the size of a 3‐packing is settled. In other cases, lower and upper bounds are obtained where mostly differ by an additive constant depending only on $k$ but one case that they differ by a linear bound in $n$.

中文翻译：

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3均匀超图中的打包群

对于正整数 $ñ\ge ķ\ge Ť$，一个集合 $\mathcal{乙}$ 的 $ķ$的子集 $ñ$-组 $X$ 被称为 $Ť$每次包装 $Ť$的子集 $X$ 最多出现在一组 $\mathcal{乙}$。在本文中，我们调查每当存在最大3个装箱时$ñ$ 足够大于 $ķ$。什么时候$ñ\not\equiv 2（模ķ-2）$，便确定了3装大小的最佳值。在其他情况下，获得下限和上限，其最大不同之处仅在于取决于$ķ$ 但一种情况是它们在 $ñ$。