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

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 , 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 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 C_t > 0 such that whenever (h ? t)(k ? t ? 1) ≥ C_t there exists an ItBD 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