#### Title

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

#### Document Type

Article

#### Publication Date

1-1-2001

#### 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. © 2001 John Wiley & Sons, Inc.

#### Publication Title

Journal of Combinatorial Designs

#### Recommended Citation

Kreher, D.,
&
Rees, R.
(2001).
A hole-size bound for incomplete t-wise balanced designs.
*
Journal of Combinatorial Designs,
9*(4), 269-284.
http://doi.org/10.1002/jcd.1011

Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3708