A Characterization of BIB Designs Based on v Treatments in Blocks of Size k Whose Number of Blocks is at Least vCk

摘要

For certain number of treatments, v, it is impossible to form a reduced BIB design in blocks of size k. Based on the necessary conditions vr = bk and lambda (v-1) = r(k-1) which must hold in any BIB (v,b,r,k, lambda) design, it is shown that v = 8 and k = 3 is the only case for which no reduced BIB design can be constructed if k > 2. A table of BIB designs for v = 8 and k = 3 with support sizes from 22 to 56 is provided. (Author)