Extremal Type II lattices of rank $72$ are generated by their second shell

Scott Duke Kominers

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arXiv · 2606.08734

Extremal Type II lattices of rank $72$ are generated by their second shell

Scott Duke Kominers

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Abstract

We show that if $L$ is an extremal Type II lattice of rank $72$, then $L$ is generated by its vectors of norm $10$. The proof determines the full inner product distribution between the shells of norms $8$ and $10$ using the spherical $11$-design property of the norm-$10$ shell.

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Scott Duke Kominers. 2026-06-07. Extremal Type II lattices of rank $72$ are generated by their second shell. https://arxiv.org/abs/2606.08734

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