The power function with Niho exponent 3q-2 is locally differentially 4-uniform over F_{q^2} for even m >= 4.
On a conjecture of differentially 8-uniform power functions,
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A class of locally differentially $4$-uniform power functions with Niho exponents
The power function with Niho exponent 3q-2 is locally differentially 4-uniform over F_{q^2} for even m >= 4.