A new ordering, extending the notion of universal cycles of Chung {\em etal.} (1992), is proposed for the blocks of $k$-uniform set systems. Existenceof minimum coverings of pairs by triples that possess such an ordering isestablished for all orders. Application to the construction of short 2-radiussequences is given, with some new 2-radius sequences found through computersearch.
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机译：提出了一种新的排序方法，扩展了Chung {\ em etal。}（1992）的通用循环的概念，用于$ k $统一集合系统的块。对于所有订单，都建立了具有这种排序的三元组对的最小覆盖的存在。给出了短2半径序列构建的应用，并通过计算机搜索发现了一些新的2半径序列。
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