Using 8-bit signed integer storage for the secret polynomial vectors in the Dilithium3 parameter set can introduce limitations in terms of precision and range of values that can be represented. The main trade-off is the potential for overflow or underflow when performing arithmetic operations on the coefficients, leading to inaccuracies in the results. To address these limitations, techniques such as careful scaling of coefficients, dynamic range adjustment during computations, and error detection and correction mechanisms can be implemented. Additionally, utilizing higher precision data types for critical operations or implementing error-checking mechanisms can help mitigate the risks associated with using 8-bit signed integers for storage.