1 research outputs found
A Completion of the spectrum of 3-way Steiner trades
A 3-way trade of volume consists of three pairwise disjoint
collections , and , each of blocks of size , such that
for every -subset of -set , the number of blocks containing this
-subset is the same in each for . If any -subset of
found() occurs at most once in each for , then is
called 3-way Steiner trade. We attempt to complete the spectrum
, the set of all possible volume sizes, for 3-way
Steiner trades, by applying some block designs, such as BIBDs, RBs, GDDs,
RGDDs, and packing grid blocks. Previously, we obtained some
results about the existence some 3-way Steiner trades. In particular,
we proved that there exists a 3-way Steiner trade of volume when
for (Rashidi and Soltankhah, 2016). Now, we show
that the claim is correct also for