A t - ( v , k , λ ) design is quasi-symmetric if there are only two block intersection sizes. We adapt the Kramer-Mesner construction method for designs with prescribed automorphism groups to the quasi-symmetric case. Using the adapted method, we find many new quasi-symmetric 2 - ( 28 , 12 , 11 ) and 2 - ( 36 , 16 , 12 ) designs, establish the existence of quasi-symmetric 2 - ( 56 , 16 , 18 ) designs, and find three new unitals 2 - ( 217 , 7 , 1 ) of non-prime power order.
['Vedran Krčadinac', 'Renata Vlahović']
New quasi-symmetric designs by the Kramer-Mesner method