Nonexistence Results for Tight Block Designs

Details Nonexistence Results for Tight Block Designs Nonexistence Results for Tight Block Designs

2011-10-16

arxiv.org/abs/1110.3463v1

Mathematics

Combinatorics

17 pages

Scientific paper

Recall that combinatorial $2s$-designs admit a classical lower bound $b \ge \binom{v}{s}$ on their number of blocks, and that a design meeting this bound is called tight. A long-standing result of Bannai is that there exist only finitely many nontrivial tight $2s$-designs for each fixed $s \ge 5$, although no concrete understanding of `finitely many' is given. Here, we use the Smith Bound on approximate polynomial zeros to quantify this asymptotic nonexistence. Then, we outline and employ a computer search over the remaining parameter sets to establish (as expected) that there are in fact no such designs for $5 \le s \le 9$, although the same analysis could in principle be extended to larger $s$. Additionally, we obtain strong necessary conditions for existence in the difficult case $s=4$.

Affiliated with

Also associated with

No associations

Rating

Nonexistence Results for Tight Block Designs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonexistence Results for Tight Block Designs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonexistence Results for Tight Block Designs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-457104