Dataset for On isomorphism and multiplier inequivalence of cyclic Steiner quadruple systems

The files contain base blocks (orbit representatives) of M-cyclic CQS(g²) for g = 20,28,40,44,52, needed for the theory of the paper "T. Dobson, T. Feng, D.F. Holt, P.R.J. Östergård, and S. Wang, On isomorphism and multiplier inequivalence of cyclic Steiner quadruple systems". A design is M-cyclic if the group of degree 2g and order 4g generated by

        (0,1,2,...,2g-1) and (1,g+1)(3,g+3)...(g-1,2g-1)

is a group of automorphisms. This group is the full automorphism group for the five designs given here. The name of a file includes the value of g.