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Sampling-based motion planners are often used to solve very high-dimensional planning problems. Many recent algorithms use projections of the state space to estimate properties such as coverage, as it is impractical to compute and store this information in the original space. Such estimates help motion planners determine the regions of space that merit further exploration. In general, the employed projections are user-defined, and to the authors' knowledge, automatically computing them has not yet been investigated. In this work, the feasibility of offline-computed random linear projections is evaluated within the context of a state-of-the art sampling-based motion planning algorithm. For systems with moderate dimension, random linear projections seem to outperform human intuition. For more complex systems it is likely that non-linear projections would be better suited.