One frame and several new infinite families of Z-cyclic whist designs Original Research Article

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(33p+1), p a prime of the form 4t+1; (2) Z-cyclic Wh(32n+1s+1), for all n⩾1, s=5,13,17; (3) Z-cyclic Wh(32ns+1), for all n⩾1, s=35,55,91; (4) Z-cyclic Wh(32n+1s), for all n⩾1, and for all s for which there exist a Z-cyclic Wh(3s) and a homogeneous (s,4,1)-DM; and (5) Z-cyclic Wh(32ns) for all n⩾1, s=5,13. Many other results are also obtained. In particular, there exist Z-cyclic Wh(33v+1) where v is any number for which Ge and Zhu obtained Z-cyclic TWh(3v+1).