caa a22 4500 445358505 CHVBK 20180317142908.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00493-011-2661-0 doi (NATIONALLICENCE)springer-10.1007/s00493-011-2661-0 Nozaki Hiroshi Graduate School of Information Sciences, Tohoku University, Aramaki-Aza-Aoba 6-3-09, 980-8579, Aoba-ku, Sendai, Japan aut Inside S -inner product sets and Euclidean designs [Elektronische Daten] [Hiroshi Nozaki] A finite set X in the Euclidean space is called an s-inner product set if the set of the usual inner products of any two distinct points in X has size s. First, we give a special upper bound for the cardinality of an s-inner product set on concentric spheres. The upper bound coincides with the known lower bound for the size of a Euclidean 2s-design. Secondly, we prove the non-existence of 2- or 3-inner product sets on two concentric spheres attaining the upper bound for any d>1. The efficient property needed to prove the upper bound for an s-inner product set gives the new concept, inside s-inner product sets. We characterize the most known tight Euclidean designs as inside s-inner product sets attaining the upper bound. János Bolyai Mathematical Society and Springer Verlag, 2011 Combinatorica Springer-Verlag 31/6(2011-12-01), 725-737 0209-9683 31:6<725 2011 31 493 https://doi.org/10.1007/s00493-011-2661-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00493-011-2661-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nozaki Hiroshi Graduate School of Information Sciences, Tohoku University, Aramaki-Aza-Aoba 6-3-09, 980-8579, Aoba-ku, Sendai, Japan aut NATIONALLICENCE 773 0- Combinatorica Springer-Verlag 31/6(2011-12-01), 725-737 0209-9683 31:6<725 2011 31 493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer