In this paper, we propose three combined Tausworthe random number generators with period length about 10¹⁸, whose k-distribution properties are good, and which can be implemented in a portable way. These generators are found through an exhaustive search for the combination with the best lattice structure in GF 2, x^k, the k-dimensional vector space over the field of all Laurent series with coefficients in GF(2). We then apply a battery of statistical tests to these generators for the comprehensive investigation of their empirical statistical properties. No apparent defect was found. In the appendix, we give a sample program in C for the generators.