We search for an isotropic stochastic gravitational-wave background (GWB) in the newly released 11 year data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). While we find no evidence for a GWB, we place constraints on a population of inspiraling supermassive black hole (SMBH) binaries, a network of decaying cosmic strings, and a primordial GWB. For the first time, we find that the GWB constraints are sensitive to the solar system ephemeris (SSE) model used and that SSE errors can mimic a GWB signal. We developed an approach that bridges systematic SSE differences, producing the first pulsar-timing array (PTA) constraints that are robust against SSE errors. We thus place a 95% upper limit on the GW-strain amplitude of AGWB \u3c 1.45 × 10−15 at a frequency of f = 1 yr−1 for a fiducial f−2/3 power-law spectrum and with interpulsar correlations modeled. This is a factor of ~2 improvement over the NANOGrav nine-year limit calculated using the same procedure. Previous PTA upper limits on the GWB (as well as their astrophysical and cosmological interpretations) will need revision in light of SSE systematic errors. We use our constraints to characterize the combined influence on the GWB of the stellar mass density in galactic cores, the eccentricity of SMBH binaries, and SMBH–galactic-bulge scaling relationships. We constrain the cosmic-string tension using recent simulations, yielding an SSE-marginalized 95% upper limit of Gμ \u3c 5.3 × 10−11—a factor of ~2 better than the published NANOGrav nine-year constraints. Our SSE-marginalized 95% upper limit on the energy density of a primordial GWB (for a radiation-dominated post-inflation universe) is ΩGWB(f) h2 \u3c 3.4 × 10−10
