On the inequalities of \(t\)-designs over a finite field. (English) Zbl 0737.05021
Some bounds on the number of blocks of \(t\)-designs over a finite field are derived. A short proof is given for the non-existence of tight \(t\)- designs over a finite field which was earlier established by L. Chihara (Applications of the Askey-Wilson polynomials to association schemes. Ph. D. Thesis, University of Minnesota, 1985).
Reviewer: K.Sinha (Ranchi)
MSC:
| 05B05 | Combinatorial aspects of block designs |
| 05E30 | Association schemes, strongly regular graphs |
References:
| [1] | Cameron, P. J., Generalisation of Fisher’s inequality to fields with more than one element, Lond. Math. Soc. Lecture Note Ser., 13, 9-13 (1974) · Zbl 0298.05018 |
| [2] | Chihara, L., Applications of the Askey-Wilson polynomials to association schemes, (Ph.D. Thesis (1985), University of Minnesota) |
| [3] | Delsarte, P., Association schemes and \(t\)-designs in regular semilattices, J. Combin. Theory, Ser. A, 20, 230-243 (1976) · Zbl 0342.05020 |
| [4] | Ray-Chaydhuri, D. K.; Wilson, R. M., On \(t\)-design, Osaka J. Math.,, 12, 737-744 (1975) · Zbl 0342.05018 |
| [5] | H. Suzuki, \(tHdq\)Hokkaido Math. J; H. Suzuki, \(tHdq\)Hokkaido Math. J |
| [6] | H. Suzuki, 2-designs over \(GF^m Graphs Combin \); H. Suzuki, 2-designs over \(GF^m Graphs Combin \) |
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