Some new families of simple t-designs

Applying some methods of construction on existing i-designs, we obtain some infinite families of new simple designs. We give a table which contains many new simple designs in small cases. The main method which is called the union method, involves taking the union of every two blocks in a given design. We also combine this method with some other well known ones. Some of the new designs obtained are the following. If there exists a Hadamard matrix of order 4m, then there exists a simple 2-(4m 1, m, m(m 1)/2) design, a 2-(4m,m,(2m-1)(m-l)) design, a simple 3-(4m,2m-l,(m-l)(2m3)) design, and a simple 3-( 4m, 2m 2, (2m 3)( m 2)( m 1)) design. Finally if q is a prime power, then there exists a simple 2_(q2(q+ 2),q(2q+ l),q(q+ 1)(2q + 1)(2q 1)/2) design. We show that the number of non-isomorphic simple 2-(15,4,6) designs is at least 10.