Measurements of the cross sections for the production of single top quarks and antiquarks in the t channel, and their ratio, are presented for proton-proton collisions at a center-of-mass energy of 13 TeV. The data set used was recorded in 2016 by the CMS detector at the LHC and corresponds to an integrated luminosity of 35.9 fb({-1}). Events with one muon or electron are selected, and different categories of jet and b jet multiplicity and multivariate discriminators are applied to separate the signal from the background. The cross sections for the t-channel production of single top quarks and antiquarks are measured to be (130±1\left(\text{stat}\right)±19\left(\text{syst}\right)\phantom{\rule{0.25em}{0ex}}\text{pb}) and (77±1\left(\text{stat}\right)±12\left(\text{syst}\right)\phantom{\rule{0.25em}{0ex}}\text{pb}), respectively, and their ratio is (1.68±0.02\left(\text{stat}\right)±0.05\left(\text{syst}\right)). The results are in agreement with the predictions from the standard model.