The Strichartz estimates for Schrödinger equations can be improved when the data is spread out in either physical or frequency space. In this paper we give refinements of the 2-dimensional homogeneous Strichartz estimate on the maximum size of a single wave packet. Different approaches are used in the proofs, including arithmetic approaches, polynomial partitioning, and the
l
2
l^2
Decoupling Theorem, for different cases. We also give examples to show that the refinements we obtain cannot be further improved when
2
≤
p
≤
4
2 \leq p \leq 4
and
p
=
6
p = 6
.