The existence of doubly near resolvable (v,3,2)‐BIBDs

Abstract

AbstractThe existence of doubly near resolvable (v,2,1)‐BIBDs was established by Mullin and Wallis in 1975. In this article, we determine the spectrum of a second class of doubly near resolvable balanced incomplete block designs. We prove the existence of DNR(v,3,2)‐BIBDs for v ≡ 1 (mod 3), v ≥ 10 and v ∉ {34,70,85,88,115,124,133,142}. The main construction is a frame construction, and similar constructions can be used to prove the existence of doubly resolvable (v,3,2)‐BIBDs and a class of Kirkman squares with block size 3, KS3(v,2,4). © 1994 John Wiley & Sons, Inc.