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Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.
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On sets spanning all subspaces of a given dimension in vector spaces over finite fields
Let $n$ be a positive integer, let $p$ be a prime, let $\mathbb F_p$ be the field with $p$ elements, and let $V = \mathbb F_p^n$ be the $n$-dimensional vector space over $\mathbb F_p$.
For an integer …