The number of repeated blocks in balanced ternary designs with block size three. II (Q1182919)

The following statement is proved: a balanced ternary design on \(v\) elements with block size three, index two, and each element repeated in precisely two blocks, and having exactly \(k\) pairs of repeated blocks exists if and only if \(v\equiv 0,2\pmod 3\), \(v\geq 5\), \(0\leq k\leq v(v- 5)/6\), and \(k\neq v(v-5)/6-1\). The proof rests on direct solutions for small cases, followed by recursive techniques.