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We present a construction of a measure-zero Kakeya-type set in afinite-dimensional space $K^d$ over a local field with finite residue field.The construction is an adaptation of the ideas appearing in [12] and [13]. Theexistence of measure-zero Kakeya-type sets over discrete valuation rings isalso discussed, giving an alternative construction to the one presented in [4]over $\mathbb{F}_q[[t]]$.

Kakeya-Type Sets in Local Fields with Finite Residue Field