4 research outputs found
On steiner spaces
AbstractA Steiner space is a Steiner triple system that is not generated by a triangle. We give new constructions of Steiner spaces and solve the existence problem of Steiner spaces of order v for all but 4 values of v
Pairwise balanced designs covered by bounded flats
We prove that for any and , there exist, for all sufficiently large
admissible , a pairwise balanced design PBD of dimension for
which all -point-generated flats are bounded by a constant independent of
. We also tighten a prior upper bound for , in which case
there are no divisibility restrictions on the number of points. One consequence
of this latter result is the construction of latin squares `covered' by small
subsquares