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    Existence of doubly near resolvable (v, 4, 3)-BIBDs

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    The existence of doubly near resolvable (v, 2, 1)-BIBDs was established by Mullin and Wallis in 1975. For doubly near resolvable (v, 3, 2)-BIBDs, the existence problem was investigated by Lamken in 1994, and completed by Abel, Lamken and Wang in 2007. In this paper, we look at doubly near resolvable (v, 4, 3)-BIBDs; we establish that these exist whenever v ≑ 1 (mod 4) except for v = 9 and possibly for v ∈{17, 213}. Further
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