A (57,14,1) strongly regular graph does not exist

Abstract We show that a strongly regular graph with parameters n =57, k =14, λ =1, ν =4 ( (0,1)-eigenvalues: 1∗14, 38∗2, 18∗(−5); (1, −1)-eigenvalues: 1∗28, 38∗(− 5), 18∗9) does not exist.