Nonexistence of nontrivial tight 8-designs

Tight t -designs are t -designs whose sizes achieve the Fisher type lower bound. We give a new necessary condition for the existence of nontrivial tight designs and then use it to show that there do not exist nontrivial tight 8-designs.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of algebraic combinatorics 2018-03, Vol.47 (2), p.301-318
1. Verfasser:	Xiang, Ziqing
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Computer Science Convex and Discrete Geometry Group Theory and Generalizations Lattices Lower bounds Mathematics Mathematics and Statistics Order Ordered Algebraic Structures
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Tight t -designs are t -designs whose sizes achieve the Fisher type lower bound. We give a new necessary condition for the existence of nontrivial tight designs and then use it to show that there do not exist nontrivial tight 8-designs.
ISSN:	0925-9899 1572-9192
DOI:	10.1007/s10801-017-0776-0