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  "body": "\n## Summary\n\nA spread of a [[projective space|ZT9A6JK8QF]] is a family of subspaces of one fixed dimension that partitions the points.\nEvery point lies in exactly one member.\nThe best known case is a spread of lines of three-dimensional space.\nSpreads matter because they build [[translation planes|JZ5J6REAMD]], through the André–Bruck–Bose construction.\n\n## Explanations\n\n### L1 human\n\nImagine filling all of space with lines so that no two lines meet and every point is on one line.\nSuch a family is a line spread.\nOver the finite field with $q$ elements, three-dimensional projective space has $(q^2 + 1)(q + 1)$ points and each line has $q + 1$ of them, so a line spread has $q^2 + 1$ lines.\nOne such spread comes from viewing pairs of elements of the field with $q^2$ elements as a four-dimensional space over the field with $q$ elements.\n",
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