EXISTENCE RESULTS FOR DOUBLY NEAR RESOLVABLE (V,3,2)-BIBDS

Let V be a set of v elements. A (1, 2; 3, v, 1)-frame F is a square ar ray of side v which satisfies the following properties. We index the r ows and columns of F with the elements of V, V = {x1, x2,..., x(v)}. ( 1) Each cell is either empty or contains a 3-subset of V. (2) Cell (x( i), x(i)) is empty for i = 1, 2,..., v. (3) Row x(i) of F contains eac h element of V- {x(i)} once and column x(i) of F contains each element of V- {x(i)} once. (4) The collection of blocks obtained from the non empty cells of F is a (v, 3,2)-BIBD. A (1, 2; 3, v, 1)-frame is a doub ly near resolvable (v, 3,2)-BIBD. In this paper, we first present a su rvey of existence results on doubly near resolvable (v, 3,2)-BIBDs and (1, 2; 3, v, 1)-frames. We then use frame constructions to provide a new infinite class of doubly near resolvable (v,3,2)-BIBDs by construc ting (1, 2; 3, v, 1)-frames.