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A DeBruijnSequence of order $n$ on a list of length $k$ is a cyclic sequence of length in which every possible block of length $n$ taken from the list occurs exactly once as a contiguous subsequence.

What algorithm(s) does DeBruijnSequence use? Why does this function run so fast even for large parameters?

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    $\begingroup$ Evaluate GeneralUtilities`PrintDefinitions[DeBruijnSequence], and you will se the code behind. $\endgroup$ Commented Aug 21 at 7:08
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    $\begingroup$ Following up on that, it seems to be driven by Language`NumbersDump`deBruijnSequencePositions which is actually a rather simple CompiledFunction that you can inspect. It appears to just be the came as the C++ implementation from Rosetta Code $\endgroup$ Commented Aug 21 at 17:54

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