3-pyramidal Steiner triple systems

A design is said to be f-pyramidal when it has an automorphism group which fixes f points and acts sharply transitively on all the others. The problem of establishing the set of values of v for which there exists an f-pyramidal Steiner triple system of order v has been deeply investigated in the case f = 1 but it remains open for a special class of values of v. The same problem for the next possible f, which is f = 3, is here completely solved: there exists a 3-pyramidal Steiner triple system of order v if and only if v = 7, 9, 15 (mod 24) or v equivalent to 3,19 (mod 48).