New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices

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 first examples of quasisymmetric designs with these parameters. The parameters belong to the families 2− (2u2−u, u2−u, u2−u−1) and 2− (2u2 +u, u2, u2−u) which are related to Hadamard parameters. The designs correspond to new codes meeting the Grey-Rankin bound.