Abstract
We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (J. Numer. Theory 4 (1972) 17). By use of these constructions, we show some constructions for regular balanced n-ary designs.
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