Abstract In 2001, Ge and Zhu published a frame construction which they utilized to construct a large class of Z -cyclic triplewhist designs. In this study the power and elegance of their methodology is illustrated in a rather dramatic fashion. Primarily due to the discovery of a single new frame it is possible to combine their techniques with the product theorems of Anderson, Finizio and Leonard along with a few new specific designs to obtain several new infinite classes of Z -cyclic whist designs. A sampling of the new results contained herein is as follows: (1) Z -cyclic Wh(3 3 p +1), p a prime of the form 4 t +1; (2) Z -cyclic Wh(3 2 n +1 s +1), for all n ⩾1, s =5,13,17; (3) Z -cyclic Wh(3 2 n s +1), for all n ⩾1, s =35,55,91; (4) Z -cyclic Wh(3 2 n +1 s ), for all n ⩾1, and for all s for which there exist a Z -cyclic Wh(3 s ) and a homogeneous ( s ,4,1)-DM; and (5) Z -cyclic Wh(3 2 n s ) for all n ⩾1, s =5,13. Many other results are also obtained. In particular, there exist Z -cyclic Wh(3 3 v +1) where v is any number for which Ge and Zhu obtained Z -cyclic TWh(3 v +1).
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