SYMMETRIC ( lOO , 45 , 20 ) - DESIGNS WITH E 25 . 53 AS FULL AUTOMORPHISM GROUP

The construction of eight nonisomorphic new symmetric (100,45,20)-designs, having E25 . S3 as their full automorphism group, is presented. 1. PRELIMINARIES Symmetric (100,45,20)-designs belong to Menon series consisting of all symmetric designs with parameters (4t2, 2t2 t, t2 t). The existence of such a design, on the basis of its equivalence with the existence of regular Hadamard matrix of order 100, has been known for a rather long time (see [3]). However, few constructions have been made so far ([2]' [5]). Here we perform a construction of designs with given parameters making use of their tactical decomposition induced by operating of the appropriate finite group. The applied method was introduced by Z. Janko, [4].