Independence number of the rank-three strongly regular graph

Determine the independence number of the unique rank-3 strongly regular graph with parameters (2048,276,44,36), equivalently prove or refute that every set of 73 distinct points in F_2^{11} contains two points whose sum is either a 23rd root of unity or a sum of two 23rd roots of unity in the construction described by the paper.

Background

The paper constructs the unique rank-3 strongly regular graph with parameters (2048,276,44,36) as Cay(γ_S), where S is a 1-cover of size 24 in F_2^{11}. The largest independent set found computationally has size 72, but no proof establishes that this is maximal.

The authors reduce the problem to showing that any 73 distinct points in F_2^{11} contain a pair whose difference, equivalently sum in characteristic two, belongs to the connection set generated by sums of two elements of S. They state that this concrete assertion remains unresolved.