Abstract
Block designs with parameters $(p^n, \Delta p^n, \Delta((p^n - 1)/2), (p^n - 1)/2, \Delta((p^n - 3)/4))$ are shown to exist whenever $p^n$, a prime power, can be expressed as $2^mt + 1$ with $m$ a positive integer and $t$ an odd integer $>1$, that is, whenever $p^n$ is not one greater than a power of 2; $\Delta$ is equal to $2^{m-1}$.
Citation
E. Nemeth. "A New Family of BIBD's." Ann. Math. Statist. 42 (3) 1118 - 1120, June, 1971. https://doi.org/10.1214/aoms/1177693343
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