Two new classes of Z-cyclic triplewhist designs
Abstract
Let q 1, q 2,... denote primes of the form 4n + 3, n ≥ 1. Until very recently there were no known examples of Z-cyclic TWh(q 1q 2q 3 + 1) and the only known examples of Z-cyclic TWh(3q 1q 2 4- 1) were contained, obscurely, in the 1896 paper of E.H.Moore. Recent results of Greig, Ge and Lam and Abel and Ge combined with the 1999 product theorems of Anderson, Finizio and Leonard provide several new examples of Z-cyclic TWh(3q 1q 2 + 1) and examples of TWh(q 1q 2q 3 + 1). Combining these latter materials with the product theorems of Anderson et al. lead to many new infinite families of Z-cyclic TWh designs. The new designs of Abel and Ge combined with the frame construction of Ge and Zhu also enable us to extend the data of Finizio and Merritt related to Z-cyclic TWh(3q ip) and TWh(3q ip 1p 2) where p,p 1,p 2 ε {5, 13, 17}.
