  Aims. The space radiation environment conditions and the maximum expected
coronal mass ejection (CME) speed are being assessed through the investigation
of scaling laws between the peak proton flux and fluence of Solar Energetic
Particle (SEP) events with the speed of the CMEs. Methods. We utilize a
complete catalog of SEP events, covering the last ~25 years of CME observations
(i.e. 1997 to 2017). We calculate the peak proton fluxes and integrated event
fluences for those events reaching an integral energy of up to E> 100 MeV,
covering the period of the last ~25 years of CME observations. For a sample of
38 strong SEP events, we first investigate the statistical relations between
the recorded peak proton fluxes (IP) and fluences (FP) at a set of integral
energies of E >10 MeV, E>30 MeV, E>60 MeV, and E>100 MeV versus the projected
CME speed near the Sun (VCME) obtained by the Solar and Heliospheric
Observatory/Large Angle and Spectrometric Coronagraph (SOHO/LASCO). Based on
the inferred relations, we further calculate the integrated energy dependence
of both IP and FP, assuming that they follow an inverse power-law with respect
to energy. By making use of simple physical assumptions, we combine our derived
scaling laws to estimate the upper limits for VCME, IP, and FP focusing on two
cases of known extreme SEP events that occurred on February 23, 1956 (GLE05)
and in AD774/775, respectively. Given physical constraints and assumptions,
several options for the upper limit VCME, associated with these events, are
investigated. Results. A scaling law relating IP and FP to the CME speed as
V^{5}CME for CMEs ranging between ~3400-5400 km/s is consistent with values of
FP inferred for the cosmogenic nuclide event of AD774/775. At the same time,
the upper CME speed that the current Sun can provide possibly falls within an
upper limit of VCME <= 5500 km/s.
