Let q1,q2,... denote primes of the form 4n + 3,n > 1. Until very recently there were no known examples of Z-cyclic lWh(q_1q_2q_3 + 1) and the only known examples of Z-cyclic TWh(3qiq2 + D were contained, obscurely, in the 1896 paper of B.H.Moore. Recen= 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-cydic TWh(3q_1q_2q_3 + 1) and examples of TWh(q_1q_2q_3+1-Combining these latter materials with the product theorems^f Anderson et al. lead to many new infinite families of Z-cychc TWh designs. The new designs of Abel and Ge combined with the frame construction of Ge and Zta also enable us to extend the data of BW and Merritt related to Z-cyclic TWh(3q_ip) and TWh(3q_ip_1p_2) where p_1,p_1, p_2 {5,13,17}.
展开▼
