Balanced Steiner triple systems

A coloring of a Steiner triple system is equitable if the cardinalities of the color classes differ by at most one. It is shown that, with the possible exceptions of v is an element of {19, 21, 37, 49, 55, 57, 67, 69, 85, 109, 139}, there exists for all v equivalent to 1, 3 (mod 6) and v greater than or equal to 15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable. (C) 1997 Academic Press.