Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG(3,3²ʰ⁺¹)

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Using a class of permutation polynomials of F₃²ʰ⁺¹ obtained from the Ree-Tits symplectic spreads in PG(3,3²ʰ⁺¹), we construct a family of skew Hadamard difference sets in the additive group of F₃²ʰ⁺¹. With the help of a computer, we show that these skew Hadamard difference sets are new when h=2 and h=3. We conjecture that they are always new when h>3. Furthermore, we present a variation of the classical construction of the twin prime power difference sets, and show that inequivalent skew Hadamard difference sets lead to inequivalent difference sets with twin prime power parameters.