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In this work we apply quasirandom sequences to develop a derivative-free algorithm for approximating the global maximum of a given function. This work is based on previous results which used a single type of quasirandom sequence in a Brute Force approach and in an approach called Localization of Search. In this work we present several methods for computing quasirandom sequences as well as measures for determining their properties. We discuss the shortcomings of the Brute Force and Localization of Search methods and then present modifications which address these issues which culminate in a new algorithm which we call Modified Localization of Search. Our algorithm is applied to a test suite of problems and the results are discussed. Finally we present some comments on code development for our algorithm.