Steiner triple systems (STSs) with subsystems of order 7 are classified. For order 19, this classification is complete, but for order 21 it is restricted to Wilson-type systems, which contain three subsystems of order 7 on disjoint point sets. The classified STSs of order 21 are tested for resolvability; none of them is doubly resolvable.

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The minimum number of codewords in a code with t ternary and b binary coordinates and covering radius R is denoted by K(t, b, R). In the paper, necessary and sufficient conditions for K(t, b, R) = M are given for M = 6 and 7 by proving that there exist exactly three families of optimal codes with six codewords and two families of optimal codes with seven codewords. The cases M 5 were settled in an earlier study by the same authors. For binary codes, it is proved that K(0, 2b + 4, b) 9 for b 1. For ternary codes, it is shown that K(3t + 2, 0, 2t) = 9 for t 2. New upper bounds obtained include K(3t + 4, 0, 2t) 36 for t 2. Thus, we have K(13, 0, 6) 36 (instead of 45, the previous best known upper bound).