All proper colorings of every colorable BSTS(15)

A Steiner System, denoted S(t, k, v), is a vertex set X containing v vertices, and a collection of subsets of X of size k, called blocks, such that every t vertices from X are in exactly one of the blocks. A Steiner Triple System, or STS, is a special case of a Steiner System where t = 2, k = 3 and v = 1 or 3 (mod6) [7]. A Bi-Steiner Triple System, or BSTS, is a Steiner Triple System with the vertices colored in such a way that each block of vertices receives precisely two colors. Out of the 80 BSTS(15)s, only 23 are colorable [1]. In this paper, using a computer program that we wrote, we give a complete description of all proper colorings, all feasible partitions, chromatic polynomial and chromatic spectrum of every colorable BSTS(15).