An even unimodular 72-dimensional lattice of minimum 8

Abstract An even unimodular 72-dimensional lattice Γ having minimum 8 is constructed as a tensor product of the Barnes lattice and the Leech lattice over the ring of integers in the imaginary quadratic number field with discriminant −7. The automorphism group of Γ contains the absolutely irreducible rational matrix group (PSL2(7) × SL2(25)) : 2.

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