#### Title

Further results on the maximum size of a hole in an incomplete t-wise balanced design with specified minimum block size

#### Document Type

Article

#### Publication Date

12-1-2002

#### Abstract

Kreher and Rees [3] proved that if h is the size of a hole in an incomplete balanced design of order v and index k having minimum block size k ≥ t + 1, then, h ≤ v + (k - t)(t - 2) - 1 k - t ) 1 : They showed that when t =2 or 3, this bound is sharp infinitely often in that for each h ≤ t and each k ≥ t ) 1, (t; h; k) = (3; 3; 4), there exists an ItBD meeting the bound. In this article, we show that this bound is sharp infinitely often for every t, viz., for each t - 4 there exists a constant Ct < 0 such that whenever (h - t)(k - t - 1) ≤ Ct there exists an ItBD meeting the bound for some γ =γ (t; h; k). We then describe an algorithm by which it appears that one can obtain a reasonable upper bound on Ct for any given value of t. © 2002 Wiley Periodicals, Inc.

#### Publication Title

Journal of Combinatorial Designs

#### Recommended Citation

Adamczak, I.,
Kreher, D.,
Ling, A.,
&
Rees, R.
(2002).
Further results on the maximum size of a hole in an incomplete t-wise balanced design with specified minimum block size.
*
Journal of Combinatorial Designs,
10*(4), 256-281.
http://doi.org/10.1002/jcd.10014

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