A Remark on Generalized Fisher Inequalities of Delsarte'st-Designs

Abstract

P. Delsarte defined the notion oft-designs inQ-polynomial association schemes and gave a Fisher type bound using linear programming. For each classical association scheme there is a geometrical interpretation of Delsarte'st-designs by a well-defined indexλ≥1,the caseλ =1giving a lower bound on the cardinality of at-design (the Singleton bound). In this paper we compare these two bounds and discuss the non-existence of tightt-designs or the lower bound of the indexλfor association schemes on sesquilinear forms.