  Background: Several previous studies provided contradicting results for the
four-neutron system, some claiming the existence of a 0+ near-threshold
resonance, others denying presence of any observable resonant states. Purpose:
Since most of the studies employed enhanced two-neutron interactions to follow
the evolution of an artificially bound state into a continuum one, we examine
several enhancement schemes that produce a bound dineutron as well. Methods: We
study the four-neutron system by solving exact four-particle equations. By
varying the interaction enhancement factor we calculate two-dineutron
scattering phase shifts and cross sections. Results: When the same enhancement
factor is used in all partial waves, a bound tetraneutron emerges together with
a strongly bound dineutron. Furthermore, such a 0+ tetraneutron evolves not
into a resonance but into a virtual state. Weak enhancement of S waves together
with strongly enhanced higher waves is needed for the emergence of the resonant
state. Anyhow the resonant behavior disappears well before reaching the
physical interaction strength. Conclusions: The interaction enhancement scheme
using the same factor for all waves, employed in several previous works, is
misleading for the search of 0+ resonance as only a virtual state can emerge.
Evolution of a bound tetraneutron into a resonance via an intermediate virtual
state is possible with strong enhancement of higher two-neutron waves.
