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We consider the existence problem for a semi-cyclic holey group divisibledesign of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD oftype (n,m^t). When t is odd and n\neq 8 or t is doubly even and t\neq 8, theexistence problem is completely solved; when t is singly even, many infinitefamilies are obtained. Applications of our results to two-dimensional balancedsampling plans and optimal two-dimensional optical orthogonal codes are alsodiscussed.

Semi-cyclic holey group divisible designs with block size three and applications to sampling designs and optical orthogonal codes