Row-column directed block designs (Q1182952)

A row-column directed balanced incomplete block designs (RCDBIBD) is a \(k\times b\) array \(A=(a_{ij})\) with element set \(V\), \(| V|=v\). For every ordered pair \((v,x)\) with \(v,x\in V\) and \(v\neq x\), there are exactly \(\lambda\) choices for \(i,j\) and \(c\) so that \(a_{ic}=v\) and \(a_{jc}=x\). In addition, every element occurs the same number of times \((\lambda(v-1)/k(k-1))\) in each row; and ordered pairs of elements occur an almost equal number of times in each row. Existence of RCDBIBD is settled for block size two, and some partial results are given for block sizes three and four.