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The progenitor system(s) as well as the explosion mechanism(s) of thermonuclear (Type Ia) supernovae are long-standing issues in astrophysics. Here we present ejecta masses and other physical parameters for 28 recent Type Ia supernovae inferred from multiband photometric and optical spectroscopic data. Our results confirm that the majority of SNe Ia show observable ejecta masses below the Chandrasekhar-limit (having a mean M ej ≈ 1.1 ± 0.3 M ⊙), consistent with the predictions of recent sub- M Ch explosion models. They are compatible with models assuming either single- or double-degenerate progenitor configurations. We also recover a sub-sample of supernovae within 1.2 M ⊙ < M ej < 1.5 M ⊙ that are consistent with near-Chandrasekhar explosions. Taking into account the uncertainties of the inferred ejecta masses, about half of our SNe are compatible with both explosion models. We compare our results with those in previous studies, and discuss the caveats and concerns regarding the applied methodology. [ABSTRACT FROM AUTHOR]