Balanced Part Ternary Designs: Some New Results

Abstract

A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say $b_2$, each having repeated elements. We prove some necessary conditions on $b_2$ and show the existence of some particular BPTDs. We also give constructions of infinite families of BPTDs with $b_1=0$, including families of ternary $t$-designs with $t\ge 3$.