The flag-transitive and point-imprimitive symmetric (v,k,λ) designs with v < 100

A complete classification of the flag-transitive point-imprimitive symmetric 2-(v,k,λ) designs with v<100 is provided. Apart from the known examples with λ⩽10, the complementary designs of PG5(2) and PG3(4), and the 2-design S−(3) constructed by Kantor in [22], we found four non-isomorphic 2-(64,28,12) designs. They were constructed via computer as developments of (64,28,12)-difference sets by AbuGhneim in [1]. In the present paper, independently from [1], we construct two of the aforementioned four 2-designs and we prove that their full automorphism group is flag-transitive and point-imprimitive. The construction is theoretical and relies on the absolutely irreducible 8-dimensional F2-representation of PSL2(7). Our result, together with that about the flag-transitive point-primitive symmetric 2-designs with v<2500 by Braić-Golemac-Mandić-Vučičić [5], provides a complete classification of the flag-transitive symmetric 2-designs with v<100.