Semiframes with Block Size Three and Odd Group Size |
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| Authors: | H Cao J Fan D Xu |
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| Affiliation: | Institute of Mathematics, Nanjing Normal University, Nanjing, China |
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| Abstract: | A  ‐semiframe of type  is a  ‐GDD of type  ,  , in which the collection of blocks  can be written as a disjoint union  where  is partitioned into parallel classes of  and  is partitioned into holey parallel classes, each holey parallel class being a partition of   for some  . A  ‐SF is a  ‐semiframe of type  in which there are p parallel classes in  and d holey parallel classes with respect to  . In this paper, we shall show that there exists a (3, 1)‐SF for any  if and only if  ,  ,  ,  and  . |
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| Keywords: | group divisible design frame semiframe Kirkman square μ ‐balanced |
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