In experiments that study social phenomena, such as peer influence or herd immunity, the treatment of one unit may influence the outcomes of others. Such "interference between units" violates traditional approaches for causal inference, so that additional assumptions are required to model the underlying social mechanism. We propose an approach that requires no such assumptions, allowing for interference that is both unmodeled and strong, with confidence intervals found using only the randomization of treatment. Additionally, the approach allows for the usage of regression, matching, or weighting, as may best fit the application at hand. Inference is done by bounding the distribution of the estimation error over all possible values of the unknown counterfactual, using an integer program. Examples are shown using a vaccine trial and two experiments investigating social influence.