Smallest defining sets for 2-(9, 4, 3) and 3-(10, 5, 3) designs

Smallest defining sets for 2-(9, 4, 3) and 3-(10, 5, 3) designs: Corrigendum

On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs

A defining set of a t-(v, k, λ) design is a partial design which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given t-design. The complete list of minimal defining sets of...

Minimal defining sets for full 2-(v, 3, v-2) designs

A t-(v, k, J\) design D = (X, B) with B = Pk(X) is called a full design. For t = 2, k = 3 and any v, we give minimal defining sets for these designs. For v = 6 and v = 7, smallest defining sets are found.

Smallest defining sets of designs associated with PG(d, 2)

For d 2:: 2, let Dd be the symmetric block design formed from the points and hyperplanes of the projective space PG(d, 2). Let 3d equal the number of blocks in a smallest defining set of Dd . The known results 32 = 3 and S3 = 9 are reviewed and it is shown that 34 = 24 and 52 :::; 35 :::; 55. If J-Ld = 3d/ (2d+ 1 1) is the proportion of blocks in a smallest defining set of Dd, then J-L2 = 3/7, ...

Smallest defining sets for 2-(10, 5, 4) designs

A set of blocks which is a subset of blocks of only one design is called a defining set of that design. In this paper we determine smallest defining sets of the 21 nonisomorphic 2-(10,5,4) designs.