  In this paper we discuss the existence problem for a semi-cyclic holey group
divisible design of type (n,m^t) with block size 3, which is denoted by a
3-SCHGDD of type (n,m^t). When n=3, a 3-SCHGDD of type (3,m^t) is equivalent to
a (3,mt;m)-cyclic holey difference matrix, denoted by a (3,mt;m)-CHDM. It is
shown that there is a (3,mt;m)-CHDM if and only if (t-1)m\equiv 0 (mod 2) and
t\geq 3 with the exception of m\equiv 0 (mod 2) and t=3. When n\geq 4, the case
of t odd is considered. It is established that if t\equiv 1 (mod 2) and n\geq
4, then there exists a 3-SCHGDD of type (n,m^t) if and only if t\geq 3 and
(t-1)n(n-1)m\equiv 0 (mod 6) with some possible exceptions of n=6 and 8. The
main results in this paper have been used to construct optimal two-dimensional
optical orthogonal codes with weight 3 and different auto- and
cross-correlation constraints by the authors recently.
