A explicit algebraic construction in high dimensions provides a counterexample showing that separated n-point sets can have diameter (1-1/π²+o(1))n² rather than the conjectured (1+o(1))n².
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Erd\H{o}s's diameter conjecture for separated distances fails in high dimensions
A explicit algebraic construction in high dimensions provides a counterexample showing that separated n-point sets can have diameter (1-1/π²+o(1))n² rather than the conjectured (1+o(1))n².