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Group testing is a long studied problem in combinatorics: A small set of r ill people should be identified out of the whole (n people) by using only queries (tests) of the form “Does set X contain an ill human?”. In this paper we provide an explicit construction of a testing scheme which is better (smaller) than any known explicit construction. This scheme has tests which is as many as the best non-explicit schemes have. In our construction we use a fact that may have a value by its own right: Linear error-correction codes with parameters [m,k,δm] _q meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in time.