A computer search over the words of weight 3 in the code of blocks of a classical Steiner triple system (STS) on 31 points is carried out to classify all STS(31) whose incidence matrix has 2-rank equal to 27, one more than the possible minimum of 26. There is a total of 1239 nonisomorphic STS(31) of 2-rank 27. Keywords Steiner triple system of 2-rank 27 · Block code of a design · Backtracking search with isomorph rejection

A parallel backtrack search is carried out to classify, up to isomorphism, all combinatorial (19 4 ) configurations. A total of 269 224 652 such configurations were found. We prove that two of the combinatorial (19 4 ) configurations are not geometrically realizable over any field. Also we confirmed the computation of the 971 171 combinatorial (18 4 ) configurations which lacked an independent verification.

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