On Block Sequences of Steiner Quadruple Systems with Error Correcting Consecutive Unions

Motivated by applications in combinatorial group testing for consecutive positives, we investigate a block sequence of a maximum packing MP(t, k, v) which contains the blocks exactly once such that the collection of all blocks together with all unions of two consecutive blocks of this sequence forms an error correcting code with minimum distance d. Such a sequence is usually called a block sequence with consecutive unions having minimum distance d, and denoted by BSCU(t, k, v|d). In this paper, we show that the necessary conditions for the existence of BSCU(3, 4, v|4)s of Steiner quadruple systems, namely, v ≡ 2, 4 (mod 6) and v ≥ 4, are also sufficient, excepting v = 8, 10.