New Classes of Perfect Maps I

The existence and construction of perfect maps, also known as de Bruijn arrays or de Bruijn tori, is further considered. A c-ary (r, s; u, v) perfect map is a two-dimensional periodic array with periods r and s and symbols from an alphabet of size c with the property that every possible u × v array of symbols occurs exactly once in a period of the array. Necessary conditions on the parameters r, s, u, v for the existence of perfect maps are known to be sufficient when c is a power of a prime. This result is combined with some generalisations of the techniques of Mitchell to construct c-ary perfect maps for a large class of parameter sets. Our results are the strongest yet obtained on the existence question for c-ary perfect maps.

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