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A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array $\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\}$ ($r, t \ge 1$), $\{135, 128, 16; 1, 16, 120\}$, $\{234, 165, 12; 1, 30, 198\}$ or $\{55, 54, 50, 35, 10; 1, 5, 20, 45, 55\}$. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. Further combinatorial arguments are then used to derive nonexistence.

Using Symbolic Computation to Prove Nonexistence of Distance-Regular Graphs