Eulerian and Hamiltonian Graphs · Hard problem

A binary de Bruijn sequence of order $3$ is a cyclic string of $8$ bits in which every $3$-bit string appears exactly once as a consecutive window (including windows that wrap around the end). For example, one such sequence is $00010111$: the windows are $000, 001, 010, 101, 011, 111, 110, 100$, and then wrapping around to $000, 001$ again. How many distinct de Bruijn sequences of order $3$ exist, counting two sequences as the same if one is a rotation of the other?