How to construct a block design with block size four admitting a blocking set

1. Introduction. Since this is a survey paper on blocking sets in block designs, the definition of a block design seems an appropriate beginning. So, here goes. A block design of index A is a pair (p, B), where P is a finite set (the elements of which are sometimes called points) and B is a collection of subsets of P (all of the same size k) called blocks such that every pair of distinct elements of P belongs to exactly blocks of B. The number Ipi = n is called the order of the block design (P, B) and, of course, the number of blocks is IBI An(n-1)/k(k-1) • Now let (P, H) be a block design. The subset X of P is called a blocking ~ if and only if for each block b s B, b n X :f i /J and b n (p " X) t-i/J. (The set X also defines a 2-colouting of (p, B) with the property that none of the blocks in B receive a monochromatic colouring. However, in what follows we will stick with calling X a blocking set rather than a 2-colouring.) The most widely studied classes of block designs are triple systems; i.e., block designs with block size 3. (See [9], for example.) Hence we begin