Cooperation in distributed settings often involves activities that must be performed at least once by the participating processors. When processor failures or delays occur, it becomes unavoidable that some tasks are done redundantly. To make efficient use of the available processors, several distributed algorithms schedule the activities of the processors in terms of permutations of tasks that need to be performed at least once. This paper presents the first explicit practical deterministic construction of sets of permutations with certain combinatorial properties that immediately make practical several deterministic distributed algorithms. These algorithms solve a variety of problems, for example, cooperation in shared-memory and message-passing settings, and the gossip problem. Prior to this work, the most efficient algorithms for some of these problems were primarily of theoretical interest — they relied on permutations that are known to exist, but very expensive to construct, with the cost of construction being at least exponential in the size of the permutations. In this paper, the explicitly constructed permutations are ultimately used directly to produce practical instances of several classes of efficient deterministic algorithms. Most importantly, for all of these algorithms, the schedule construction cost is reduced from exponential to polynomial, at the expense of slight detuning, at most polylogarithmic, of the efficiency of these algorithms.