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(Abridged) Surveys of protoplanetary disks in nearby star-forming regions(SFRs) have provided important information on their demographics, but due totheir sample sizes, they cannot be used to study how disk properties vary withthe environment. We conduct a survey of the unresolved millimeter continuumemission of 873 protoplanetary disks identified by Spitzer in the L1641 andL1647 regions of the Orion A cloud. This is the largest such survey yet,allowing us to identify even weak trends in the median disk mass as a functionof position in the cloud and cluster membership. The sample detection rates andmedian masses are also compared to those of nearby (<300 pc) SFRs. The samplewas observed with ALMA at 225 GHz, with a median rms of 0.08 mJy/beam (1.5M$_{\oplus}$). The data were reduced and imaged using an innovative paralleldata processing approach. We detect 58% (502/873) of the observed disks. Thisincludes 20 disks with dust masses >100 M$_{\oplus}$, and two objectsassociated with extended dust emission. We infer a median disk dust mass in thefull sample of $2.2^{+0.2}_{-0.2}$ M$_{\oplus}$. In L1641 and L1647 median dustmasses are $2.1^{+0.2}_{-0.2}$ M$_{\oplus}$ and $2.6^{+0.4}_{-0.5}$M$_{\oplus}$, respectively. The disk mass distribution of the full sample issimilar to that of nearby low-mass SFRs at similar ages of 1-3 Myr. We findonly weak trends in disk (dust) masses with galactic longitude and between theYSO clusters identified in the sample, with median masses varying by $\lesssim$50%. Age differences may explain these median disk mass variations. Apart fromthis, disk masses are essentially constant at scales of ~100 pc. This alsosuggests that the majority of disks, even in different SFRs, are formed withsimilar initial masses and evolve at similar rates, assuming no externalirradiation, with disk mass loss rates of $\sim 10^{-8}$ M$_{\odot}$/yr.

Survey of Orion Disks with ALMA (SODA) I: Cloud-level demographics of 873 protoplanetary disks