On the switching construction of Steiner quadruple systems

The structure of Steiner quadruple system S(v, 4, 3) of full 2-rank v− 1 is considered. It is shown that there are two types (induced and singular) of such systems. It is shown that induced Steiner systems can be obtained from Steiner systems S(v, 4, 3) of 2-rank v − 2 by switching construction which is introduced here. Moreover, all non-isomorphic induced Steiner systems S(16, 4, 3) of full 2rank 15 are enumerated. It is found that there are 305616 such non-isomorphic systems S(v, 4, 3), which are obtained from all 708103 non-isomorphic such systems of rank 14 studied earlier.