Parameters for a class of partially balanced incomplete block designs with two associate classes are immediately implied by the triangular association scheme. This paper deals with the more difficult question of whether or not these parameters imply the triangular association scheme.
"The Uniqueness of the Triangular Association Scheme." Ann. Math. Statist. 29 (1) 262 - 266, March, 1958. https://doi.org/10.1214/aoms/1177706724