Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Jordi Marzo Sánchez[en] This project is a study of Chebyshev-type quadratures and the theory behind these mathematical objects, as well as an analysis of some of the most recent results in relation to optimal quadratures. The main purpose is to understand the solution of the Korevaar-Meyers conjecture by Bodarenko, Radchenko and Viazovska. Furthermore, some sphere sampling tools necessary for the proof will also be discussed.