This paper presents a method for correlating the octane numbers of fuel mixtures, and applies this to the study of toluene reference fuels (TRFs) blended with ethanol. This method combines linear regression and exhaustive (or brute-force) searching for optimal Scheffe polynomials, where optimality is defined as the shortest polynomial that meets a reasonable estimate of the reproducibility limits in the standard, octane number test procedures. Two correlations for the RON and MON are found to be optimal. These achieve maximum absolute errors (MAE) of less than 2 octane numbers across TRF/ethanol mixtures with a RON between 80 and 120. These two correlations use mole fractions as the correlating variables, are consistent with previously published, linear TRF correlations, and show that binary (non-linear) interactions between iso-octane/ethanol, n-heptane/ethanol and toluene/ethanol are all significant. The use of liquid volume fractions is also shown to lead to poor correlation performance, thereby demonstrating the superiority of mole fractions as the correlating variables. (C) 2016 Elsevier Ltd. All rights reserved.