Generalized spikes with circuits and cocircuits of different cardinalities

We consider matroids with the property that every subset of ground set size s is contained in a 2s-element circuit and t 2t-element cocircuit. say such matroid has (s,2s,t,2t)-property. A an (s,t)-spike if there partition into pairs union any Our main result all sufficiently large (s,2s,t,2t)-property are (s,t)-spikes, generalizing 2019 proved case where s=t. also present some properties (s,t)-spikes.