In this paper we show that for any integer n ≥ 1, primes p1, ..., pn, pi ≡ 3 (mod 4), pi > 3, i = 1, ..., n, and all nonnegative integers r, r1, ..., rn there exist Hadamard matrices of special Williamson kind and difference sets of order 4 × 32r ×...
