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The Baksan Experiment on Sterile Transitions (BEST) probes the galliumanomaly and its possible connections to oscillations between active and sterileneutrinos. Based on the Gallium-Germanium Neutrino Telescope (GGNT) technologyof the SAGE experiment, BEST employs two zones of liquid Ga target to exploreneutrino oscillations on the meter scale. Oscillations on this short scalecould produce deficits in the $^{71}$Ge production rates within the two zones,as well as a possible rate difference between the zones.  From July 5th to October 13th 2019, the two-zone target was exposed to aprimarily monoenergetic, 3.4-MCi $^{51}$Cr neutrino source 10 times for a totalof 20 independent $^{71}$Ge extractions from the two Ga targets. The $^{71}$Geproduction rates from the neutrino source were measured from July 2019 to March2020. At the end of these measurements, the counters were filled with $^{71}$Gedoped gas and calibrated during November 2020. In this paper, results from theBEST sterile neutrino oscillation experiment are presented in details. Theratio of the measured $^{71}$Ge production rates to the predicted rates for theinner and the outer target volumes are calculated from the known neutrinocapture cross section. Comparable deficits in the measured ratios relative topredicted values are found for both zones, with the $4 \sigma$ deviations fromunity consistent with the previously reported gallium anomaly. If interpretedin the context of neutrino oscillations, the deficits give best fit oscillationparameters of $\Delta m^2=3.3^{+\infty}_{-2.3}$ eV$^2$ and sin$^22\theta=0.42^{+0.15}_{-0.17}$, consistent with $\nu_e \rightarrow \nu_s$oscillations governed by a surprisingly large mixing angle.

A Search for Electron Neutrino Transitions to Sterile States in the BEST Experiment