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A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.
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Vandermonde matrices and general position
Not quite what you are asking for but I think these concepts are related.
First: Is it $k\geq n$ or $k\leq n$. Are $S_i$ disjoint?. If $k < n $ There is a property called restricted orthonormality pro …