New quasi-symmetric designs constructed

Using Hadamard matrices and mutually orthogonal Latin squares, we construct two new quasi-symmetric designs, with parameters 2 (66; 30; 29) and 2 (78; 36; 30). These are the rst examples of quasi- symmetric designs with these parameters. The parameters belong to the families 2 (2u 2 u; u 2 u; u 2 u 1) and 2 (2u 2 +u; u 2 ; u 2 u) which are related to Hadamard parameters. The designs correspond to new codes meeting the Grey-Rankin bound.