The problem of finding the optimum tapped delay line (TDL) gain settings for a digital communications receiver with a detection process involving a single threshold level (zero volts) is examined. Based on a minimax criterion which seeks to maximize the eye opening-to-rms noise ratio, an optimum set of tap gains is found with the aid of a geometric construction inn-dimensional space. An iterative procedure for calculating the tap gains is derived from then-dimensional space concepts. With some slight modifications, the same procedure is used to obtain the optimum TDL when the detection process involves two threshold levels(\pm E volts). The optimization scheme described by Lucky is also given a geometric interpretation so that the two methods can be compared; in some cases, they yield identical results.