Asaspecialshift-invariantspaces,splinesubspacesyieldmanyadvantagessothattherearemanypracticalapplicationsforsignalorimageprocessing.Inthispaper,wepayattentiontothesamplingandreconstructionprobleminsplinesubspaces.Weimprovelowerboundofsamplingsetconditionsinsplinesubspaces.Basedontheimprovedexplicitlowerbound,aimprovedexplicitconvergenceratioofreconstructionalgorithmisobtained.Theimprovedconvergenceratiooccupiesfasterconvergenceratethanoldone.Attheend,somenumericalexamplesareshowntovalidateourresults.