Elkies, NoamKominers, Scott2011-11-222010Elkies, Noam, and Scott Kominers. 2010. Refined configuration results for extremal type II lattices of ranks 40 and 80. Proceedings of the American Mathematical Society 138(1): 105-108.0002-99391088-6826http://nrs.harvard.edu/urn-3:HUL.InstRepos:5351639We show that, if \(L\) is an extremal Type II lattice of rank 40 or 80, then \(L\) is generated by its vectors of norm \(min(L)+2\). This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms \(min(L)\) and \(min(L)+2\).en-USType II latticeextremal latticeweighted theta functionspherical designconfiguration resultJournal Article2011-11-2210.1090/S0002-9939-09-10063-1