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

5-16-2002

Department

Department of Mathematical Sciences

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.

Publisher's Statement

© 2002 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.10014

Publication Title

Journal of Combinatorial Designs

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