A computer-implemented method for detecting the presence or absence of a fetal aneuploidy, comprising: (a) obtaining partial nucleotide sequence reads from a test sample comprising circulating cell-free nucleic acid from a pregnant female bearing a fetus, wherein at least some of the partial nucleotide sequence reads comprise: i) multiple nucleobase gaps between identified nucleobases, wherein the partial nucleotide sequence reads are unary partial reads, wherein in said unary partial reads one nucleotide species is known at known positions and the other positions can be any one of three other nucleotide species, or wherein the partial nucleotide sequence reads are ternary partial reads, wherein in said ternary partial reads a first nucleotide species is known at known positions, a second nucleotide species is known at other known positions and the other positions are any one of two nucleotide species other than the first nucleotide species and the second nucleotide species; or ii) one or more nucleobase classes, wherein each nucleobase class comprises a subset of nucleobases present in the sample nucleic acid, wherein the partial nucleotide sequence reads are binary partial reads, for which binary partial reads a first nucleotide class consisting of two possible bases is known at known positions and a second nucleotide class consisting of two possible bases is known at known positions, wherein the bases of the first nucleotide class are different than the bases of the second nucleotide class; or a combination of (i) and (ii), and wherein the first nucleobase class is purine and the second nucleobase class is pyrimidine, (b) mapping the partial nucleotide sequence reads to genomic sections of a reference genome, (c) counting the number of partial nucleotide sequence reads mapped to each genomic section, (d) normalizing the counts of the partial nucleotide sequence reads according to guanine and cytosine content of the genomic sections, thereby providing normalized counts, (e) comparing the normalized counts to a reference, thereby making a comparison, and (f) detecting the presence or absence of a fetal aneuploidy based on the comparison. (a) obtaining partial nucleotide sequence reads from a test sample comprising circulating cell-free nucleic acid from a pregnant female bearing a fetus, wherein at least some of the partial nucleotide sequence reads comprise: i) multiple nucleobase gaps between identified nucleobases, wherein the partial nucleotide sequence reads are unary partial reads, wherein in said unary partial reads one nucleotide species is known at known positions and the other positions can be any one of three other nucleotide species, or wherein the partial nucleotide sequence reads are ternary partial reads, wherein in said ternary partial reads a first nucleotide species is known at known positions, a second nucleotide species is known at other known positions and the other positions are any one of two nucleotide species other than the first nucleotide species and the second nucleotide species; or ii) one or more nucleobase classes, wherein each nucleobase class comprises a subset of nucleobases present in the sample nucleic acid, wherein the partial nucleotide sequence reads are binary partial reads, for which binary partial reads a first nucleotide class consisting of two possible bases is known at known positions and a second nucleotide class consisting of two possible bases is known at known positions, wherein the bases of the first nucleotide class are different than the bases of the second nucleotide class; or a combination of (i) and (ii), and wherein the first nucleobase class is purine and the second nucleobase class is pyrimidine, i) multiple nucleobase gaps between identified nucleobases, wherein the partial nucleotide sequence reads are unary partial reads, wherein in said unary partial reads one nucleotide species is known at known positions and the other positions can be any one of three other nucleotide species, or wherein the partial nucleotide sequence reads are ternary partial reads, wherein in said ternary partial reads a first nucleotide species is known at known positions, a second nucleotide species is known at other known positions and the other positions are any one of two nucleotide species other than the first nucleotide species and the second nucleotide species; or ii) one or more nucleobase classes, wherein each nucleobase class comprises a subset of nucleobases present in the sample nucleic acid, wherein the partial nucleotide sequence reads are binary partial reads, for which binary partial reads a first nucleotide class consisting of two possible bases is known at known positions and a second nucleotide class consisting of two possible bases is known at known positions, wherein the bases of the first nucleotide class are different than the bases of the second nucleotide class; or (b) mapping the partial nucleotide sequence reads to genomic sections of a reference genome, (c) counting the number of partial nucleotide sequence reads mapped to each genomic section, (d) normalizing the counts of the partial nucleotide sequence reads according to guanine and cytosine content of the genomic sections, thereby providing normalized counts, (e) comparing the normalized counts to a reference, thereby making a comparison, and (f) detecting the presence or absence of a fetal aneuploidy based on the comparison.