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

TL;DR

This paper investigates the existence of semi-cyclic holey group divisible designs with block size three, providing complete solutions for certain parameter cases and applications to sampling plans and optical codes.

Contribution

It completely solves the existence problem for specific parameter cases and constructs many infinite families for singly even t, advancing design theory and its applications.

Findings

Complete existence results for certain parameter cases.

Construction of many infinite families for singly even t.

Applications to sampling plans and optical orthogonal codes.

Abstract

We consider 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 t is odd and n\neq 8 or t is doubly even and t\neq 8, the existence problem is completely solved; when t is singly even, many infinite families are obtained. Applications of our results to two-dimensional balanced sampling plans and optimal two-dimensional optical orthogonal codes are also discussed.