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Block designs for symmetric parallel line assays with block size odd. (English) Zbl 1193.62140
Summary: In a parallel line assay, there are three treatment contrasts of major importance. Block designs allowing the estimability of all the three contrasts free from block effects, called $$L$$-designs, necessarily have even block sizes. For odd block sizes, we provide a class of highly efficient designs, called nearly $$L$$-designs. These nearly $$L$$-designs have been constructed by establishing a link with linear and nearly linear trend-free designs.

##### MSC:
 62K10 Statistical block designs
##### Keywords:
linear trend-free designs; nearly $$L$$-designs
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