I read about single-shot error correction using 3D gauge color codes. I saw the claim that it enables significant qubit and time overhead improvement regarding 2D surface codes, since it does not require several syndrome-measurements. However, since this gauge color code is already a 3D structure, just as the 2+1D of surface code with repeating syndrome measurement, why does it save qubits or time?
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Well, it can save time, since you can (in principle) perform all the syndrome measurements in parallel. But as you point out, it does not obviously save in (space $\times$ time).
