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The conditions under which matrix orientifolding and supersymmetrytransformations commute are known to be stringent. Here we present the casespossessing four or eight supercharges upon ${\bf Z}_3$ orbifolding followed bymatrix orientifolding. These cases descend from the matrix models with eightplus eight supercharges. There are fifty in total, which we enumerate.Comment: 17pages; references adde

Matrix orientifolding and models with four or eight supercharges