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Betten, Anton
Designs, codes, and cryptography, 06/2016, Letnik: 79, Številka: 3Journal Article
Packings of 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 PG ( 3 , 2 ) give rise to two of seven solutions of Kirkman’s problem. Here, we continue the problem of classifying packings of PG ( 3 , q ) by settling the case q = 3 . We find that there are exactly 73,343 packings of PG ( 3 , 3 ) .
