Existence of Incomplete Transversal Designs with Block Size Five and Any Index λ

The basic necessary condition for the existence of a TD(5, λ; v)-TD(5, λ; u), namely v ≥ 4u, is shown to be sufficient for any λ ≥ 1, except when (v, u) = (6, 1) and λ = 1, and possibly when (v, u) = (10, 1) or (52, 6) and λ = 1. For the case λ = 1, 86 new incomplete transversal designs are constructed. Several construction techniques are developed, and some new incomplete TDs with block size six and seven are also presented.

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