An even unimodular 72-dimensional lattice of minimum 8

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 $(\PSL_2(7) \times \SL _2(25)) : 2$.

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