Unimodular Hunting II

TL;DR

This paper classifies unimodular lattices of ranks 28 and 29 under specific conditions, extending previous work and providing a detailed understanding of their isometry classes.

Contribution

It determines the isometry classes of unimodular lattices of rank 28 and 29 with certain norm restrictions, advancing the classification of these lattices.

Findings

Complete classification of rank 28 unimodular lattices.

Identification of unimodular lattices of rank 29 without short vectors.

Extension of previous classification results.

Abstract

Pursuing ideas in a recent work of the second author, we determine the isometry classes of unimodular lattices of rank 28, as well as the isometry classes of unimodular lattices of rank 29 without nonzero vectors of norm <=2.