Existence Of Doubly Near Resolvable (Nu, 4, 3)-Bibds

The existence of doubly near resolvable (nu, 2, 1)-BIBDs was established by Mullin and Wallis in 1975. For doubly near resolvable (nu, 3, 2)-BIBDs, the existence problem was investigated by Lamken in 1994, and completed by Abel, Lamken and Wang in 2007. In this paper, we look at doubly near resolvable (nu, 4, 3)-BIBDs; we establish that these exist whenever nu 1 ( mod 4) except for nu = 9 and possibly for nu is an element of{17, 213}. Further, when nu is not an element of{5, 9, 17, 185, 205, 213}, our designs are also (1, 3; 4)-frames of type 1(nu).