Constructing Large Nearly Orthogonal Sets over Finite Fields

For every prime p, there exists a constant δ > 0 such that for every field F of characteristic p and for all integers k ≥ 2 and d ≥ k, there exists a k-nearly orthogonal set of at least dδ·k/ log k vectors in Fd. The size of this set is optimal up to the log k term in the exponent.