# On Designs (or Packings)

## Time:

Friday, 11 December 2009 (All day)

## Venue:

• A-212 (STCS Seminar Room)

I will give 3 proofs for showing, There exists a family of subsets $\mathfrak{F}$, of $\{ 1 \cdots n\}$,

1. such that each element $A \in \mathfrak{F}$ is of size $\frac{n}{4}$
2. for any pair $A,B \in \mathfrak{F}$, $|A \cap B| \leq \frac{n}{8}$
3. and $|\mathfrak{F}| = 2^{\Omega(n)}$