The blue noise or ‘void-and-cluster’ dither pattern avoids directional artefacts while retaining the optimal qualities of the Bayer pattern. The Bayer matrix can in fact be derived from the void-and-cluster generation algorithm itself[8].
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The efficiency depends on the query size relative to the data distribution. A small query in a sparse region prunes almost everything. A query that covers the whole space prunes nothing (because every node overlaps), degenerating to a brute-force scan. The quadtree gives you the most benefit when your queries are spatially local, which is exactly the common case for map applications, game physics, and spatial databases.
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