On the Number of Sets in a Null t-Design

In this paper we prove that the symmetric difference of any two distinct Sλ (n, k, t) Steinersystems contains at least 2t+i different sets (Corollary 2). The proof also yields an extremal set theoretical result of Sauer (Theorem 2).

[1]  Alexander Rosa,et al.  Steiner triple systems having a prescribed number of triples in common , 1975 .

[2]  Shuo-Yen Robert Li,et al.  On the Structure of t-Designs , 1980, SIAM J. Algebraic Discret. Methods.

[3]  Peter Frankl,et al.  On the Trace of Finite Sets , 1983, J. Comb. Theory, Ser. A.

[4]  Norbert Sauer,et al.  On the Density of Families of Sets , 1972, J. Comb. Theory A.

[5]  P. Frankl,et al.  On the vector space of 0-configurations , 1982, Comb..

[6]  Jack E. Graver,et al.  The Module Structure of Integral Designs , 1973, J. Comb. Theory, Ser. A.