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

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

A set of blocks which can be completed to exactly one t-(v, k, A) design is called a defining set of that design. A known algorithm is used to determine all smallest defining sets of the 11 non-isomorphic 2-(9,4,3) designs. Nine of the designs have smallest defining sets of eight blocks each; the other two have smallest defining sets of six blocks each. Various methods are then used to find all...

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...

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

Super-simple 2-(v, 5, 1) directed designs and their smallest defining sets

In this paper we investigate the spectrum of super-simple 2-(v, 5, 1) directed designs (or simply super-simple 2-(v, 5, 1)DDs) and also the size of their smallest defining sets. We show that for all v ≡ 1, 5 (mod 10) except v = 5, 15 there exists a super-simple (v, 5, 1)DD. Also for these parameters, except possibly v = 11, 91, there exists a super-simple 2-(v, 5, 1)DD whose smallest defining s...

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.