As usual this is a set of anomalous experimental data from one lab group that could not be repeated by others and had been shown to be due to faulty experimental methods.Einstein argued that the general covariance of his theory of gravity supports Mach's principle, which would eliminate any "absolute motion" within general relativity. However, as pointed out by Willem de Sitter in 1916, Mach's principle is not completely fulfilled in general relativity because there exist matter-free solutions of the field equations. This means that the "inertio-gravitational field", which describes both gravity and inertia, can exist in the absence of gravitating matter. However, as pointed out by Einstein, there is one fundamental difference between this concept and absolute space of Newton: the inertio-gravitational field of general relativity is determined by matter, thus it is not absolute.
Miller, Dayton C. (1933). "The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth". Reviews of Modern Physics. 5 (3): 203–242. Bibcode:1933RvMP....5..203M. doi:10.1103/RevModPhys.5.203
Rev. Mod. Phys. 27, 167 (1955) - New Analysis of the Interferometer Observations of Dayton C. Miller