We have measured weak antilocalization effects, universal conductance fluctuations, and Aharonov-Bohm oscillations in the two-dimensional electron gas formed in InGaAs/AlInAs heterostructures. This system possesses strong spin-orbit coupling and a high Land�� factor. Phase-coherence lengths of 2$-$4 $��$m at 1.5$-$4.2 K are extracted from the magnetoconductance measurements. The analysis of the coherence-sensitive data reveals that the temperature dependence of the decoherence rate complies with the dephasing mechanism originating from electron-electron interactions in all three experiments. Distinct beating patterns superimposed on the Aharonov-Bohm oscillations are observed over a wide range of magnetic fields, up to 0.7 Tesla at the relatively high temperature of 1.5 K. The possibility that these beats are due to the interplay between the Aharonov-Bohm phase and the Berry one, different for electrons of opposite spins in the presence of strong spin-orbit and Zeeman interactions in ring geometries, is carefully investigated. It appears that our data are not explained by this mechanism; rather, a few geometrically-different electronic paths within the ring's width can account for the oscillations' modulations.