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What's the most efficient decomposition in terms of T-count of the 4-qubit Toffoli with 1 ancilla?

Just for posterity, the construction in the paper you referenced can be improved from $32n \pm O(1)$ to $16n \pm O(1)$, without using feedback and while still using only one ancilla: Note that all ...
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What's the most efficient decomposition in terms of T-count of the 4-qubit Toffoli with 1 ancilla?

The best known decomposition of the CCCX gate into Clifford+T (allowing feedback) uses 6 T gates: https://arxiv.org/abs/2106.11513
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