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In pulse position modulation (PPM) communications an acquisition sequence is needed to establish frame synchronization for subsequent data transmission. This sequence must have PPM structure (one pulse per frame) and desirable autocorrelation properties for its detection. The problem of finding aperiodic PPM acquisition sequences having the minimum possible autocorrelation for all off-shifted positions is investigated. Sequences with the maximum possible number of frames have been found up to frame size . Examples are given for every frame length up to , and powers of two up to . An interesting relation between the PPM sequence problem, Costas and sonar arrays, and Golomb's ruler is explored.