Minimal homogeneous Steiner 2-(v,3)(v,3) trades

A Steiner 2-(v,3)(v,3) trade is a pair (T1,T2)(T1,T2) of disjoint partial Steiner triple systems, each on the same set of vv points, such that each pair of points occurs in T1T1 if and only if it occurs in T2T2. A Steiner 2-(v,3)(v,3) trade is called d-homogeneous if each point occurs in exactly d   blocks of T1T1 (or T2T2). In this paper we construct minimal d  -homogeneous Steiner 2-(v,3)(v,3) trades of foundation vv and volume dv/3dv/3 for sufficiently large values of vv. (Specifically, v>3(1.75d2+3)v>3(1.75d2+3) if vv is divisible by 3 and v>d(4d/3+1+1)v>d(4d/3+1+1) otherwise.)