Combined Intra- and Inter- Block Analysis of Balanced Ternary Designs

Note on parameters of balanced ternary designs

Conditions under which constant block size implies constant replication number and vice versa are established for balanced ternary designs. This note is motivated by a note of almost the identical title of W. D. Wallis [2]. In a balanced binary design with constant block size, the replication number must be constant, but the converse is not true. Wallis [2] proved the following partial converse...

Nested balanced ternary designs and Bhaskar Rao designs

In this paper, we consider balanced ternary designs, BTDs, in which every block contains one element singly and the rest doubly. We call these packed BTDs, and we investigate three aspects of these designs: existence, nestings and signings. Construction methods generate classes of packed BTDs that are nested with balanced (BIBD) or partially balanced (PBIBD) incomplete block designs. Some of th...

Balanced part ternary designs: some new results

A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say b2, each having repeated elements. We prove some necessary conditions on b2 and show the existence of some particular BPTDs. We also give constructions of infinite families of BPTDs with b1 = 0, including families of ternary t-designs with t ≥ 3.

Splitting balanced incomplete block designs

Balanced ternary designs with holes and numbers of common triples

There exists a balanced ternary design with block size 3 and index 2 on 2v P2 + 4 and 2v P2 + 1 elements with a hole of size v, for all positive integers v and P2, such that v ~ 2P2 + 1. As an application of this result, we determine the numbers of common triples in two simple balanced ternary designs with block size 3 and index 2, for P2 = 3 and 4.