On the number of repeated triples in balanced ternary designs with index two

Abstract

There exists a balanced ternary design with block size 3 and index 2 on 2ν - ρ₂ + 1 and 2ν - ρ₂ + 4 elements with a hole of size ν, for all positive integers ν and ρ₂, ν ≥ 2ρ₂ + 1, having a prescribed number of repeated triples. As an application of this result, we determine the possible number of repeated triples in a balanced ternary design with index 2, for ρ₂ = 3 and 4.