Skew‐orthogonal steiner triple systems

Case studies and new results in combinatorial enumeration

“…designs can be generated directly but the resulting algorithm is orders of magnitude slower than the presented extension techniques. For example, we found it to be more than 100 times slower to generate the 4763 nonisomorphic 3- (8,4,9) designs using this direct approach. On the other hand, we discovered that for each value of !…”

“…For example, a trivial modi®cation to the rules for inducing forbidden blocks allowed us to discover the very ®rst anti-FM TTS (12). For de®nitions and further details, the reader is referred to the article by Dukes and Mendelsohn [9].…”

“…A result by Spence listed in [29] indicates that there are exactly 5,201,971 nonisomorphic 2- (8,42,21,4,9) BIBDs. We in fact enumerated a total of 8,360,901 designs, and this result has subsequently been con®rmed by Spence.…”