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We describe the techniques we developed to efficiently find the most fault-tolerant flat XOR-based erasure codes for storage systems. These techniques substantially reduce the search space for finding fault-tolerant codes (e.g., by a factor of over 52 trillion in one case). This reduction in the search space has allowed us to find the most fault-tolerant codes for larger codes than was previously thought feasible. The result of our effort to find the most fault-tolerant flat XOR-based erasure codes for storage systems has yielded a corpus of 49,215 erasure codes that we are making public.