For a multiple access communication system it is desirable to have a set of sequences such that (a) each sequence has as peaky an auto-correlation as possible and (b) each pair of sequence has as negligible a cross-correlation as possible. Peakiness of the auto-correlation of a sequence is measured in terms of its discrimination, which is to be maximized. The negligibility of a cross-correlation is judged on the basis of the energy in the cross-correlation which is to be minimized. The satisfaction of the criterion (a) is achievable by maximizing the discrimination of the sequence having its minimum value in the set. The performance along the criterion (b) is improved by seeking to minimize the maximum value of the energy of the cross correlation among all pairs of sequences. These are two established optimization problems, first of a maxmin type and the second of a minimax type. In this work they are combined into a single optimization problem by Simonization, a procedure introduced earlier for simpler situations. Sets of four binary sequences of lengths up to 1000 have been obtained by combinatorial search based on non-local optimization techniques such as Hamming scan, Backtracking, and Sidetracking, introduced earlier in simpler contexts.