In this work we present an algorithm to construct sparse-paving matroids over finite set S. From this algorithm we derive some useful bounds on the cardinality of the set of circuits of any Sparse-Paving matroids which allow us to prove in a simple way an asymptotic relation between the class of Sparse-paving matroids and the whole class of matroids. Additionally we introduce a matrix based method which render an explicit partition of the r-subsets of S, S r = ⊔ γ i=1 Ui such that each Ui defines a sparse-paving matroid of rank r.
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