Some self-blocking block designs (Q909657)

A balanced incomplete block design D is said to be self-blocking if (i) the blocking sets of minimum cardinality of D form a block design \(D^ c\) and (ii) the blocking sets of minimum cardinality of \(D^ c\) are precisely the blocks of D. In this paper it is shown that the classical projective planes \(PG(2,q^ 2)\) and the classical affine planes AG(2,q) (with \(q\geq 4\) in the latter case) are self-blocking. PG(2,3) and PG(2,5) are also shown to be self-blocking. The development of the material is nicely interlarded with remarks which set the results obtained in a historical context.