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I was reading about Luby-Rackoff theorem from various sources: [1], [2], [3], which says you need at least 3 rounds of a $2$-branch Feistel network to get a PRP if the underlying $f$ function is a PRF. I also came to know about the Generalized Feistel Network which has more than two branches.

My question:

What will be the minimum number of rounds to get a PRP from a generalized $n~(>2)$ branch Feistel network, given the underlying function $f$ is a PRF?

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