Covering pairs by quintuples: The case v congruent to 3 (mod 4)

Let C(v) denote the least number of quintuples of a v-set V with the property that every pair of distinct elements of V occurs in at least one quintuple. Let B(v) = ⌈v⌈(v − 1)/4⌉/5⌉. It is shown that C(15 = B(15) + 1, and that if v congruent to 3 (mod 4), v ⩾ 7 and v ≠ 15, then C(v) = B(v).

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