Bounds for generalized triple-array deviation

Determine how the minimum common width parameter ω(r × c, v) for generalized triple arrays can be bounded in terms of r, c, and v, where ω(r × c, v) is the least integer ω for which an (r × c, v; ω_rc, ω_rr, ω_cc)-generalized triple array exists with all three widths at most ω.

Background

Generalized triple arrays relax the near triple-array requirement by allowing intersection sizes to range over more than two consecutive values. The paper introduces ω(r × c, v) as the smallest uniform width permitting such a design, but does not derive general bounds for this quantity. The concluding question asks for bounds expressed through the array dimensions and number of symbols.