Further results on the maximum size of a hole in an incomplete t-wise balanced design with specified minimum block size
✍ Scribed by I. Adamczak; D. L. Kreher; A. C. H. Ling; R. S. Rees
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 192 KB
- Volume
- 10
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
Abstract
Kreher and Rees 3 proved that if h is the size of a hole in an incomplete balanced design of order υ and index λ having minimum block size $k \ge t+1$, then,
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 I__t__BD 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 C~t~ > 0 such that whenever (h − t)(k − t − 1) ≥ C~t~ there exists an I__t__BD meeting the bound for some λ = λ(t,h,k). We then describe an algorithm by which it appears that one can obtain a reasonable upper bound on C~t~ for any given value of t. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 256–281, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10014