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We present three families of minimal border rank tensors: they come fromhighest weight vectors, smoothable algebras, or monomial algebras. We analysethem using Strassen's laser method and obtain an upper bound $2.431$ on$\omega$. We also explain how in certain monomial cases using the laser methoddirectly is less profitable than first degenerating. Our results form possiblepaths in the search for valuable tensors for the laser method away fromCoppersmith-Winograd tensors.

Bounds on complexity of matrix multiplication away from CW tensors