On the Cardinality Spectrum and the Number of Latin Bitrades of Order 3

@article{Krotov2019OnTC,
  title={On the Cardinality Spectrum and the Number of Latin Bitrades of Order 3},
  author={Denis S. Krotov and Vladimir N. Potapov},
  journal={Probl. Inf. Transm.},
  year={2019},
  volume={55},
  pages={343-365}
}
By a (latin) unitrade, we call a set of vertices of the Hamming graph that is intersects with every maximal clique in $0$ or $2$ vertices. A bitrade is a bipartite unitrade, that is, a unitrade splittable into two independent sets. We study the cardinality spectrum of the bitrades in the Hamming graph $H(n,k)$ with $k=3$ (ternary hypercube) and the growth of the number of such bitrades as $n$ grows. In particular, we determine all possible (up to $2.5\cdot 2^n$) and large (from $14\cdot 3^{n-3… 
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