Abstract
The support of a BIB design is the set of all distinct blocks in the design. The notation BIB(v,b,r,k,λ|b ∗) is used to denote a BIB( v, b, r, k, λ) design with precisely b ∗ distinct blocks inthe design. New lower bounds on b ∗ are obtained by utilizing the information about those blocks in the support that are repeated λ times in the design. These results on the support together with other new and old results are used: 1. (1) To show the nonexistence of BIB(8,56t,21t,3,6t|b ∗) designs with b ∗≤21 , the design with the support size of 22 being already available. 2. (2) To show the nonexistence of BIB(11,55t,15t,3,3t|b ∗) designs with b ∗≤24 , and moreover, to show the existence of a BIB(11,55,15,3,3|25) design by actual construction. 3. (3) To construct a BIB(12,44,11,3,2|28) design. This design has the minimum support size within the family of BIB(12,44 t,11 t,3,2 t) designs.
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