General existence conjecture for near triple arrays

Establish that an (r × c, v)-near triple array exists for every integer r ≥ 3, every c ≥ r(r − 1), and every v ≥ c.

Background

The paper proves existence for three-row near triple arrays whenever c ≥ 6 and v ≥ c, and proves that for r ≥ 4 no (r × (r(r−1)−1), r(r−1)+1)-near triple arrays exist. These results motivate the proposed threshold c = r(r−1) as the point beyond which existence might hold uniformly for all v ≥ c. The statement is explicitly presented as a conjecture.