In this work we show how a vector-valued version of Schechtman's empirical
method can be used to reduce the number of inputs in a nonlocal game G while
preserving the quotient β∗(G)/β(G) of the quantum over the classical
bias. We apply our method to the Khot-Vishnoi game, with exponentially many
questions per player, to produce another game with polynomially many (N≈n8) questions so that the quantum over the classical bias is Ω(n/log2n)