| Abstract: | Abstact: 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  and  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  and a second infinite family of designs with parameters  where m is any positive integer. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 72–78, 2001 |
