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The packings of \(\mathrm{PG}(3,3)\)

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Abstract

Packings of \(\mathrm{PG}(3,q)\) are closely related to Kirkman’s problem of the 15 schoolgirls from 1850 and its generalizations: Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast. The packings of \(\mathrm{PG}(3,2)\) give rise to two of seven solutions of Kirkman’s problem. Here, we continue the problem of classifying packings of \(\mathrm{PG}(3,q)\) by settling the case \(q=3.\) We find that there are exactly 73,343 packings of \(\mathrm{PG}(3,3)\).

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  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Anton Betten

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  1. Anton Betten
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Correspondence to Anton Betten.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.

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Betten, A. The packings of \(\mathrm{PG}(3,3)\) . Des. Codes Cryptogr. 79, 583–595 (2016). https://doi.org/10.1007/s10623-015-0074-6

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