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A simple, recently observed generalization of the classical Singleton boundto list-decoding asserts that rate $R$ codes are not list-decodable usinglist-size $L$ beyond an error fraction $\tfrac{L}{L+1} (1-R)$ (the Singletonbound being the case of $L=1$, i.e., unique decoding). We prove that in orderto approach this bound for any fixed $L >1$, one needs exponential alphabets.Specifically, for every $L>1$ and $R\in(0,1)$, if a rate $R$ code can belist-of-$L$ decoded up to error fraction $\tfrac{L}{L+1} (1-R -\varepsilon)$,then its alphabet must have size at least $\exp(\Omega_{L,R}(1/\varepsilon))$.This is in sharp contrast to the situation for unique decoding where certainfamilies of rate $R$ algebraic-geometry (AG) codes over an alphabet of size$O(1/\varepsilon^2)$ are unique-decodable up to error fraction$(1-R-\varepsilon)/2$.  Our lower bound is tight up to constant factors in the exponent -- with highprobability random codes (or, as shown recently, even random linear codes) over$\exp(O_L(1/\varepsilon))$-sized alphabets, can be list-of-$L$ decoded up toerror fraction $\tfrac{L}{L+1} (1-R -\varepsilon)$.

AG codes have no list-decoding friends: Approaching the generalized Singleton bound requires exponential alphabets