The Existence of Two Pairwise Additive BIBD(v, 2, 1) for Any v
The existence of additive balanced incomplete block (BIB) designs has been discussed with direct and recursive constructions in Sawa et al. (2006). In this article, pairwise additive BIB designs are proposed and then new recursive methods of constructing such designs are provided. It is finally shown that for any integer v, two pairwise additive B(v, 2, 1) can be constructed. As a by-product we present a recursive construction of multiply nested BIB designs of block sizes 2ℓ for some ℓ.
KeywordsIncidence matrix Balanced incomplete block (BIB) design Additive BIB design Pairwise additive BIB design Nested BIB design Multiply nested BIB design Ordered design Perpendicular array
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