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Landsberg used such techniques to give nontrivial equations for the tensors of border rank at most $2m-3$ in $K^m\\otimes K^m\\otimes K^m$ if $m$ is even. He also gave such equations for tensors of border rank at most $2m-5$ in $K^m\\otimes K^m\\otimes K^m$ if $m$ is odd. 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