Cd3As2 is a candidate three-dimensional Dirac semimetal which has exceedingly high mobility and nonsaturating linear magnetoresistance that may be relevant for future practical applications. We report magnetotransport and tunnel diode oscillation measurements on Cd3As2, in magnetic fields up to 65 T and temperatures between 1.5 and 300 K. We find that the nonsaturating linear magnetoresistance persists up to 65 T and it is likely caused by disorder effects, as it scales with the high mobility rather than directly linked to Fermi surface changes even when approaching the quantum limit. From the observed quantum oscillations, we determine the bulk three-dimensional Fermi surface having signatures of Dirac behavior with a nontrivial Berry phase shift, very light effective quasiparticle masses, and clear deviations from the band-structure predictions. In very high fields we also detect signatures of large Zeeman spin splitting (g∼16).