Discrete choice experiments (DCEs) are frequently used to estimate and forecast the behavior of an individual's choice. DCEs are based on stated preference; therefore, underlying experimental designs are required for this type of study. According to psychologists, DCE designs consist of a small number of choice sets with a limited size in the number of alternatives within a choice set to increase the response efficiency in the questionnaire. Even though algorithmic constructions (known as efficient designs) become quite common for practitioners, optimal designs (sometimes so-called orthogonal designs) continue to be used in choice experiment studies, particularly in the case that prior information about the extent of the population preference is not available. Various approaches have been developed to construct DCE designs with fewer choice sets. However, the question in many practitioners' minds is which techniques perform better (i.e. given small designs with high efficiency) in a given circumstance. In this paper and to address these concerns, we conducted an overview of the constructions of discrete choice experiments in the literature for models with only main effects. The various ways of constructing optimal and near-optimal designs were compared in terms of their ability to minimize the number of choice sets in the survey. Our findings shed light on the optimal sample sizes needed for efficient experimentation which then can help the researchers to design more effective experiments in this area.