On the inequality for bibds with special parameters

For a .-resolvable Balanced Incomplete Block Design (BIBD) with parameters v, b = mt, r = . t, k and ., Kageyama (1973) obtained an inequality b . v + t - 1.The main purpose of this note is to improve b . v + t - 1 to b . max {v + t - 1, (m2. + m)/.2}.This inequality is also improved further for a .-resolvable BIBD which is not affine .-resolvable.