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We place statistical constraints on Type Ia supernova (SN Ia) progenitorsusing 227 nebular phase spectra of 111 SNe Ia. We find no evidence of strippedcompanion emission in any of the nebular phase spectra. Upper limits are placedon the amount of mass that could go undetected in each spectrum using recenthydrodynamic simulations. With these null detections, we place an observational$3\sigma$ upper limit on the fraction of SNe Ia that are produced through theclassical H-rich non-degenerate companion scenario of < 5.5%. Additionally, weset a tentative $3\sigma$ upper limit on He star progenitor scenarios of <6.4%, although further theoretical modelling is required. These limits refer toour most representative sample including normal, 91bg-like, 91T-like, and"Super Chandrasekhar" \sne but excluding SNe Iax and SNe Ia-CSM. As part of ouranalysis, we also derive a Nebular Phase Phillips Relation, which approximatesthe brightness of a SN Ia from $150-500$~days after maximum using the peakmagnitude and decline rate parameter $\Delta m_{15} (B)$.

Nebular Spectra of 111 Type Ia Supernovae Disfavor Single Degenerate Progenitors