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In this article we construct maximal partial 2-spreads in PG(8,q) of deficiency δ = (k − 1) ⋅ q2, where k ≤ q2 + q + 1 and δ = k ⋅ q2 + l ⋅ (q2 − 1) + 1, where k + l ≤ q2 and δ = (k + 1) ⋅ q2 + l ⋅ (q2 − 1) + m ⋅ (q2 − 2) + 1, where k + l + m ≤ q2. Using these results, we also construct maximal partial 2-spreads in PG(3m − 1,q) of various deficiencies for m ≥ 4.
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