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Create prj file for local grid from control points in local grids and known grid

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Hi, I have 18 control points in both a local grid and AGD66 zone 55. We know the local grid is also in the same datum (AGD66). I'm wondering how I can create a prj file for the local grid from the control points.

I followed a Creating a Local Mine Projection on esri forum but the result is not good enough, the largest 'error' is about 23 meters between a control point in local grid and the one in AGD66 zone 55. Not sure if something I did wrong or maybe the central_meridian and latitudeof origin I entered is in AGD66 rather than GDA94? Any advise would be appreciated.

regards,
Jack

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