KTS(45) with automorphisms
of order 15
The resolutions
of cyclic STS(45)s invariant under the subgroup of
order 15 of the cyclic automorphism group of order 45 are written in 17 files. This
is because they have in total 32 966 147 resolutions. Each cyclic STS(45)s has between 87 and 23737 such resolutions.
The record
about each cyclic STS(45) starts with "d"
and the number which we assigned to this design, then "R" is followed
by the consecutive number of its resolution, next after “A” the order of its
full automorphism group is given, "cyc" is followed
by 1 if the resolution is point-cyclic and by 0 otherwise. Only 2128 point-cyclic
KTS(45) have full automorphism group of order 45. All
the remaining resolutions are with full automorphism group of order 15.
In the second
line, the number of parallel class orbits under the subgroup of order 15 of the
cyclic automorphism group of order 45 for this resolution is given. A base
class of each of them is given in one of the following lines, where the lines
begin with the class length followed by the numbers of the blocks of the base
class.