Block designs with large holes and α ‐resolvable BIBDs

In a ( v, k , λ: w ) incomplete block design (IBD) (or PBD [ v, {k, w * }. λ]), the relation v ≥ ( k − 1) w + 1 must hold. In the case of equality, the IBD is referred to as a block design with a large hole, and the existence of such a configuration is equivalent to the existence of a λ‐resolvable BIBD( v − w, k − 1, λ). The existence of such configurations is investigated for the case of k = 5. Necessary and sufficient conditions are given for all v and λ ≢ 2 (mod 4), and for λ ≡ 2 mod 4 with 11 possible exceptions for v . © 1993 John Wiley & Sons, Inc.