Constructions of simple Mendelsohn designs

Doubly equivalent designs

Mendelsohn and Liang, in J. Combin. Des. 11 (2003), introduced a new class of difference sets and designs: (v, k, [λ1, λ2, . . . , λm])-difference sets and (v, k, [λ1, λ2, . . . , λm])-designs, and mainly discussed designs with a relationship called λ-equivalence. In this paper, we introduce the concepts of a doubly equivalent design as well as a super class. We describe the structure of super ...

Simple 3-designs and PSL(2, q) with q == 1 (mod 4)

In this paper, we consider the action of (2, q) on the finite projective line Fq ∪ {∞} for q ≡ 1 (mod 4) and construct several infinite families of simple 3-designs which admit PSL(2, q) as an automorphism group. Some of the designs are also minimal. We also indicate a general outline to obtain some other algebraic constructions of simple 3-designs.

The existence of resolvable Mendelsohn designs RMD({3, s*}, v)

Perfect Mendelsohn designs with block size six

Super-simple balanced incomplete block designs with block size 4 and index 5

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v, 4, λ)-BIBDs have been determined for λ = 2, 3, 4 and 6. When λ = 5, the necessary conditions of such a d...