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Constant and Nearly Constant Block-Sum Partially Balanced Incomplete Block Designs and Magic Rectangles
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Journal Article
Constant and Nearly Constant Block-Sum Partially Balanced Incomplete Block Designs and Magic Rectangles
2023
Overview
We illustrate that the magic rectangles and magic rectangle sets are essentially constant block-sum partially balanced incomplete block designs in disguise. Further, nearly constant block-sum partially balanced incomplete block-sum designs are defined and obtained for the special class when
r
=
1
,
λ
1
=
1
and
λ
2
=
0
.
It is shown that these are the best designs minimizing the corrected sum of squares due to block-sums. A short catalog of these designs is provided. Thus, these constant or nearly constant block-sum partially balanced incomplete block designs can be constructed for any number of blocks and any block sizes except 2.
Publisher
Springer International Publishing,Springer Nature B.V
