Existence of near resolvable (v, k, k-1) BIBDs with k∈{9, 12, 16}

A necessary condition for existence of a (v, k, k−1) near resolvable BIBD is v ≡ 1 (mod k). In this paper, we update earlier known existence results when k ∈ {9, 12, 16}, and show this necessary condition is sufficient, except possibly for 26, 37 and 149 values of v for k = 9, 12, 16 respectively. Some new results for existence of (9, 8)-frames of type 9 are also obtained; in particular, we show these exist for all t ≥ 139.

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