GDDs with two groups of unequal sizes and block size four

<p>We obtain several results towards the proof that the necessary conditions are sufficient for the existence of a GDD<span class="math inline">\((n_1 = 1, n_2 = n, 4; \lambda_1, \lambda_2)\)</span> where <span class="math inline">\(\lambda_1 \ge \lambda_2\)</span>. We also have some general results including the constructions for larger block sizes as well as when the first group size <span class="math inline">\(n_1\)</span> is not 1 or <span class="math inline">\(\lambda_1 < \lambda_2\)</span>.</p>