Abstract
Hall and Connor ( Canad. J. Math. 6 (1954) , 35–41) give iff conditions for a residual design to be embeddable in a symmetrical design. This article gives the corresponding theorem and proof for derived designs and uses this theorem to complete a BIBD (15, 35, 14, 6, 5) ( Hall, “Combinatorial Theory,” Ginn (Blaisdell), Boston, p. 295, #83; Rao, ( Sankhyā 23 (1961) , 117–127), #62) to 13 non-isomorphic SBIBD (36, 15, 6)s. Several of these symmetric designs have the trivial automorphism group, and one of them provides an example of a SBIBD (36, 21, 12) with a symmetric incidence matrix that has all 0s on the diagonal.
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