Z-cyclic (t,8)GWhD(v), t=2,4

Generalized whist tournament designs are resolvable or near-resolvable $(v,k,k-1)$-designs in which each block of size $k=et$ is partitioned into $e$ teams of $t$ players each; every two players appear in exactly $t-1$ games as teammates and in exactly $k-t$ games as opponents. In this paper the cases when $k=8$ and $t \in \{2,4\}$ are treated under the additional assumption that the design is cyclic or 1-rotational (that is, ${\Bbb Z}$-cyclic). Existence is settled affirmatively when $v=7p+1$ and $p\equiv 1 \pmod{8}$ is a prime, with two exceptions. Consequences for the existence of other whist tournament designs are examined.