caa a22 4500 469075090 CHVBK 20180323132933.0 cr unu---uuuuu 170328e19920801xx s 000 0 eng 10.1007/BF02293039 doi (NATIONALLICENCE)springer-10.1007/BF02293039 On the covering multiplicity of lattices [Elektronische Daten] [J. Conway, N. Sloane] Let the lattice Λ have covering radiusR, so that closed balls of radiusR around the lattice points just cover the space. The covering multiplicityCM(Λ) is the maximal number of times the interiors of these balls overlap. We show that the least possible covering multiplicity for ann-dimensional lattice isn ifn≤8, and conjecture that it exceedsn in all other cases. We determine the covering multiplicity of the Leech lattice and of the latticesI n, An, Dn, En and their duals for small values ofn. Although it appears thatCM(I n)=2 n−1 ifn≤33, asn → ∞ we haveCM(I n)∼2.089... n . The results have application to numerical integration. Springer-Verlag New York Inc., 1992 Conway J. Mathematics Department, Princeton University, 08540, Princeton, NJ, USA aut Sloane N. Mathematical Sciences Research Center, AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA aut Discrete & Computational Geometry Springer New York 8/2(1992-08-01), 109-130 0179-5376 8:2<109 1992 8 454 https://doi.org/10.1007/BF02293039 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02293039 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Conway J. Mathematics Department, Princeton University, 08540, Princeton, NJ, USA aut NATIONALLICENCE 700 1- Sloane N. Mathematical Sciences Research Center, AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA aut NATIONALLICENCE 773 0- Discrete & Computational Geometry Springer New York 8/2(1992-08-01), 109-130 0179-5376 8:2<109 1992 8 454 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer