Abstract-Upper and lower bounds are presented for the maximal possible size of mixed binary/ternary error-correcting codes. A table up to length 13 is included. The upper bounds are obtained by applying the linear programming bound to the product of two association schemes. The lower bounds arise from a number of different constructions.

A collection C of k-subsets (called blocks) of a v v-set Xðv vÞ ¼ f1; 2; . . . ; v vg (with elements called points) is called a t-ðv v; k; m; Þ covering if for every m-subset M of Xðv vÞ there is a subcollection K of C with jKj ! such that every block K 2 K has at least t points in common with M. It is required that v v ! k ! t and v v ! m ! t. The minimum number of blocks in a t-ðv v; k; m; Þ covering is denoted by C ðv v; k; t; mÞ. We present some constructions producing the best known upper bounds on C ðv v; k; t; mÞ for k ¼ 6, a parameter of interest to lottery players.

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A binary code C C_ ] with M codewords is called an (n, M, r, it) multiple covering of the farthest-off points (MCF) if the Hamming spheres of radius r centered at the codewords cover the whole space ] and. every x E ] such that d(x, C) r is covered by at least it codewords.The minimum possible cardinality F(n, r, it) of such a code is studied and tables of upper bounds on F(n, r, it) for n _ 16, r _ 4, it _ 4 are given.

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