A hole-size bound for incomplete t-wise balanced designs

Document Type

Article

Publication Date

6-1-2001

Department

Department of Mathematical Sciences

Abstract

An incomplete t-wise balanced design of index λ is a triple (X,H,B) where X is a v-element set, H is a subset of X called the hole, and B is a collection of subsets of X called blocks, such that, every t-element subset of X is either in H or in exactly λ blocks, but not both. If H is a hole in an incomplete t-wise balanced design of order v and index λ, then \H\ ≤ v/2 if t is odd and \H\ ≤ (v - 1)/2 if t is even. In particular, this result establishes the validity of Kramer's conjecture that the maximal size of a block in a Steiner t-wise balanced design is at most v/2 if t is odd and at most (v - 1)/2 when t is even.

Publisher's Statement

© 2001 John Wiley & Sons, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.1011

Publication Title

Journal of Combinatorial Designs

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