Automorphism bound for the q=5 multispread

Prove or refute the conjecture that every projective 3-(152,5,{2})_5 system has at most three automorphisms.

Background

The authors searched for projective 3-(26+126,5,{2})_5 systems by first examining faithful projective 2-(26,5,2,1)_5 systems with prescribed automorphism groups. They found many such systems but none that could be completed to the desired multispread. On this computational basis, they formulate an explicit conjecture limiting the automorphism-group size of any hypothetical example.

References

We conjecture that if a projective $3$-$(26{+}126,5,{2})_5$ system exists, then it has at most~$3$ automorphisms.

— Generalized ovals, 2.5-dimensional additive codes, and multispreads  (2511.15843 - Krotov et al., 19 Nov 2025) in Section 4, “Multispreads in PG(4,q),” subsection “q=5”