  More than 40 years ago, Schroeppel and Shamir presented an algorithm that
solves the Subset Sum problem for $n$ integers in time $O^*(2^{0.5n})$ and
space $O^*(2^{0.25n})$. The time upper bound remains unbeaten, but the space
upper bound has been improved to $O^*(2^{0.249999n})$ in a recent breakthrough
paper by Nederlof and W\k{e}grzycki (STOC 2021). Their algorithm is a clever
combination of a number of previously known techniques with a new reduction and
a new algorithm for the Orthogonal Vectors problem. In this paper, we improve
the space bound by Nederlof and W\k{e}grzycki to $O^*(2^{0.246n})$ and also
simplify their algorithm and its analysis. We achieve this by using an idea,
due to Howgrave-Graham and Joux, of using a random prime number to filter the
family of subsets. We incorporate it into the algorithm by Schroeppel and
Shamir and then use this amalgam inside the representation technique. This
allows us to reduce an instance of Subset Sum to a larger number of instances
of weighted orthogonal vector.
