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{\bf K. Mackenzie-Fleming}
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{\bf An infinite Family of Non-embeddable Hadamard Designs}
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The parameters $2$ - $(2\lambda+2,\lambda+1,\lambda)$ are those of a residual
Hadamard $2$ - $(4\lambda+3,2\lambda+1,\lambda)$ design. All $2$ - $(2\lambda+2,\lambda+1,\lambda)$
designs with $\lambda \le 4$ are embeddable. The existence of non-embeddable
Hadamard $2$-designs has been determined for the cases $\lambda = 5$, $\lambda =
 6$,
and $\lambda = 7$. In this paper the existence of an infinite family of
non-embeddable $2$ - $(2\lambda+2,\lambda+1,\lambda)$ designs,
$\lambda = 3(2^m) - 1, m \ge 1$ is
established.


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