Near Optimal Hardness of Approximating 2-Prover-1-Round Games with Small Alphabet Size

For all ε > 0, it is NP-hard to distinguish whether a 2-Prover-1-Round projection game with alphabet size q has value at least 1-δ or at most 1/q^(1-ε), establishing a nearly optimal alphabet-to-soundness tradeoff for 2-query PCPs.