Maximal arcs and quasi-symmetric designs

Abstract

We show that the construction of quasi-symmetric designs with parameters 2-$$(q^3, q^{2}(q-1)/2, q(q^3 -q^2 -2)/4)$$(q3,q2(q-1)/2,q(q3-q2-2)/4) and block intersection numbers $$q^{2}(q-2)/4$$q2(q-2)/4 and $$q^{2}(q-1)/4$$q2(q-1)/4 (where $$q \ge 4$$q?4 is a power of 2) given by Blokhuis and Haemers (J Stat Plan Inference 95:117---119, 2001) leads to exponential numbers of such designs. For $$q=4$$q=4, there are already at least 28,844 isomorphism classes.