Comparison of the Bounds for the Block Intersection Number of Incomplete Block Designs

Firstly, we give a complete comparison between Agrawal's bounds (1964a) and Shah's bounds (1965) given for the block intersection number of incomplete block designs. That is, it is asserted that Agrawal's bound is generally superior to that given by Shah for certain partially balanced incomplete bloCk (PBIB) designs validating Shah's bounds. Secondly, we compare Agrawal's bound with another general bound for the block intersection numer.