Summary: ``In this paper, we introduce a method of constructing universal cycles on sets by taking `sums' and `products' of smaller cycles. We demonstrate this new approach by proving that if there exist universal cycles on the 4-subsets of [18] and the 4-subsets of [26], then for any integer $n\ge18$ equivalent to $2 \pmod 8$, there exists a universal cycle on the 4-subsets of [n].''