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We construct six new explicit families of linear maximum sum-rank distance(MSRD) codes, each of which has the smallest field sizes among all known MSRDcodes for some parameter regime. Using them and a previous result of theauthor, we provide two new explicit families of linear partial MDS (PMDS) codeswith smaller field sizes than previous PMDS codes for some parameter regimes.Our approach is to characterize evaluation points that turn extended Moorematrices into the parity-check matrix of a linear MSRD code. We then producesuch sequences from codes with good Hamming-metric parameters. The six newfamilies of linear MSRD codes with smaller field sizes are obtained using MDScodes, Hamming codes, BCH codes and three Algebraic-Geometry codes. The MSRDcodes based on Hamming codes, of minimum sum-rank distance $ 3 $, meet a recentbound by Byrne et al.

A general family of MSRD codes and PMDS codes with smaller field sizes from extended Moore matrices