Bush-type Hadamard matrices and symmetric designs

A symmetric 2-(100,45,20) design is constructed that admits a tactical decomposition into 10 point and block classes of size 10 such that every point is in either 0 or 5 blocks from a given block class, and every block contains either 0 or 5 points from a given point class. This design yields a Bush-type Hadamard matrix of order 100 that leads to two new infinite classes of symmetric designs with parameters nu = 100(81(m) + 81(m-1) +...+ 81 + 1), kappa = 45(81)(m), lambda = 20(81)(m) and nu = 100(121(m) + 121(m-1) +...+ 121 + 1), kappa = 55(121)(m), lambda = 30(121)(m), where m is an arbitrary positive integer Similarly, a Bush-type Hadamard matrix of order 36 is constructed and used for the construction of an infinite family of designs with parameters nu = 36(25(m) + 25(m-1) +...+ 51 + 1), k = 15(25)(m), lambda = 6(25)(m) and a second infinite family of designs with parameters nu = 36(49(m) + 49(m-1) +...+ 49 + 1, k =21(49)(m), lambda = 12(49)m where m is any positive integer. (C) 2000 John Wiley & Sons. Inc.