On three-designs of small order

For positive integers t=0. Wilson has shown that there exists a constant N(t, k, v) such that designs B"t[k,@l;v] exist provided @l>N(t,k,v) and @l satisfies the trivial necessary conditions. We show that N(3,k,v)=0 for most of the cases under consideration and we give a numerical upper bound on N(3, k, v) for all 3=

[1]  Spyros S. Magliveras,et al.  t-Designs from the large Mathieu groups , 1981 .

[2]  Richard M. Wilson,et al.  An Existence Theory for Pairwise Balanced Designs II. The Structure of PBD-Closed Sets and the Existence Conjectures , 1972, J. Comb. Theory, Ser. A.

[3]  E. Witt.  über Steinersche Systeme , 1937 .

[4]  D. R. Hughes,et al.  On t-Designs and Groups , 1965 .

[5]  Richard M. Wilson,et al.  An Existence Theory for Pairwise Balanced Designs, III: Proof of the Existence Conjectures , 1975, J. Comb. Theory, Ser. A.

[6]  Peter J. Cameron.  Extending Symmetric Designs , 1973, J. Comb. Theory, Ser. A.

[7]  Haim Hanani,et al.  Balanced incomplete block designs and related designs , 1975, Discret. Math..

[8]  Haim Hanani,et al.  On Some Tactical Configurations , 1963, Canadian Journal of Mathematics.

[9]  Sanpei Kageyama,et al.  THE FAMILY OF t-DESIGNS* - PART II , 1980 .

[10]  Richard M. Wilson,et al.  An Existence Theory for Pairwise Balanced Designs II. The Structure of PBD-Closed Sets and the Existence Conjectures , 1972, J. Comb. Theory A.

[11]  R. Carmichael,et al.  Introduction to the theory of groups of finite order , 1908 .

[12]  R. H. F. Denniston,et al.  Some New 5-Designs , 1976 .

[13]  H. Mattson,et al.  New 5-designs , 1969 .

[14]  J. A. Todd,et al.  A representation of the Mathieu groupM24 as a collineation group , 1966 .

[15]  E. Witt,et al.  Die 5-fach transitiven gruppen von mathieu , 1937 .

[16]  William O. Alltop.  Extending t-Designs , 1975, J. Comb. Theory, Ser. A.