Explicit sets of cardinality 2'o of p-adic numbers which are algebraically independent over Qp are constructed. Let Qp be the p-adic completion of Q for a prime p. Let Qp be the algebraic closure of Qp, and Cp be its p-adic completion which is an algebraically closed field of cardinality 2"O . Let Qunram be the maximum unramiQp fied extension field of Qp. Then Qpunra = QP (W), where W is the set of all roots of unity whose orders are prime to p. Let Cunram be the p-adic closure p of Qunram in C,. Koblitz [1] asked whether Cunram has uncountably infinite transcendence degree over Qp and Cp has uncountably infinite transcendence degree over Cunram. Lampert [2] answered that the transcendence degree of p Cunram over Qp is 2tO and the transcendence degree of Cp over C unram is 2No by constructing sets of algebraically independent numbers of cardinality 2NO. Here we will give more explicit examples of such sets which cannot be obtained by the method in [2]. Theorem. Let K be an intermediate field between Qp and C P. Let ca 1' C.am be in Cp and a,, ... 5 aXnI be algebraically independent over K. Suppose that for i = 1, ... ,m 1 there exist sequences {flik}k>1 in Cp converging to a and a sequence {Sk}k>i of finite subsets of Aut(CP/K({1,lk}l