Bergé, Anne-Marie; Martinet, Jacques Symmetric groups and lattices. (English) Zbl 1132.11329 Monatsh. Math. 140, No. 3, 179-195 (2003). Summary: This paper deals with various problems in lattice theory involving local extrema. In particular, we construct infinite series of highly symmetric spherical 3-designs which include some of the examples constructed by J. Martinet and B. Venkov [in: Euclidean lattices, spherical designs and modular forms. On the works of Boris Venkov. Monogr. Enseign. Math. 37, 112–134 (2001; Zbl 1131.11344)] in dimensions 5 and 7. We also construct new types of dual-extreme lattices. Cited in 3 Documents MSC: 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 11H56 Automorphism groups of lattices Keywords:local extrema; infinite series of highly symmetric spherical 3-designs; dual-extreme lattices Citations:Zbl 1131.11344 PDFBibTeX XMLCite \textit{A.-M. Bergé} and \textit{J. Martinet}, Monatsh. Math. 140, No. 3, 179--195 (2003; Zbl 1132.11329) Full Text: DOI