The Rouquier dimension of the category of perfect complexes over a regular ring

We show that the Rouquier dimension of the category of perfect complexes over a regular ring is precisely the Krull dimension of the ring. Previously, it was known that the Krull dimension is an upper bound, the lower bound however was not known in general. In particular, for regular local rings this result is new. More generally, we show that a lower bound of the Rouquier dimension is given by the maximal length of a regular sequence.