Mastermind

Abstract

LetV(n, k) denote the set of vectors of lengthn whose components are integersj with 1≦j≦k. For every two vectorsx, y inV(n, k), leta(x, y) stand for the number of subscriptsi withx _i =y _i . We prove that for every positive ε there is ann(ε) with the following property: ifn>n(ε) andk<n ^1−ε then there is a setQ of at most (6+ε)(n logk)/(logn−logk) vectors inV(n, k) such that for every two distinct vectorsx, y inV(n, k) someq inQ hasa(q, x) ≠a(q, y).