Abstract
In this paper, we give constructions of block designs with block size 4 and index λ, for λ = 3, 6 which have a blocking set for all admissible orders (with at most 5 possible exceptions). A design which admits a blocking set is 2-colorable. These results, in conjunction with an earlier paper [1], settle the existence question for 2-colorable block designs with block size 4 for all λ (with a handful of possible exceptions).
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