Partial geometric designs and two-class partially balanced designs

Partial geometric designs and difference families

We examine the designs produced by different types of difference families. Difference families have long been known to produce designs with well behaved automorphism groups. These designs provide the elegant solutions desired for applications. In this work, we explore the following question: Does every (named) design have a difference family analogue? We answer this question in the affirmative ...

Balanced Nested Designs and Balanced n-ary Designs

We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (1972). By use of these constructions, we show some constructions for regu...

Partial Difference Sets and Partially Balanced Weighing Designs for Calibration and Tournaments

E-optimal Semi-regular Graph Designs and Partially Efficiency Balanced Designs

Jacroux (1985) extended the definition of Regular graph designs of Mitchell and John (1976) to Semi-regular graph (SRG) designs, and studied the type 1 optimality of block designs. Here, the construction and optimality of some more SRG designs are discussed. Moreover, in this investigation, it is established that a class of two associate partially efficiency balanced design is, in fact SRG desi...

On construction of partially balanced n-ary designs

A new method of constructing a series of partially balanced ternary (PBT) designs is presented. In the method, we have added the corresponding rows of incidence matrices of a BIB design and a PBIB design, both obtained from single initial block with at least one element in common between them. The BIB and PBIB designs above were obtained by method of differences. We have also constructed PBT de...