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This paper presents new constructions of multistage wave-mixing networks with arbitrary b×b space-switching elements, where b ≥ 2. In these networks, for a size of F fiber links and W wavelengths per link, converter requirements are O(FlogbW) or O(FW/b) for rearrangeable nodes, and O(FlogbWlogb(FW)) or O(FWlogb(FW)/b) for different types of strictly nonblocking nodes inspired from the Cantor topology. In all cases, the worst case number of cascaded conversion is O(logbW). When b=W ≤ F, the required number of converters, and the worst case number of cascaded conversions are respectively O(F) and O(1), and are both optimal up to a constant. The new networks generalize and improve upon previous wave-mixing networks based on 2×2 space switches.