The purpose of this note is to show that the existence of any one of a particular family of four partially balanced incomplete block designs (pbibd) implies the existence of the remaining three designs. A sufficient condition for the existence of this family is given and a nonexistence result is also obtained.
"On a Class of Partially Balanced Incomplete Block Designs." Ann. Math. Statist. 36 (6) 1807 - 1814, December, 1965. https://doi.org/10.1214/aoms/1177699810