Abstract
A finite net N of degree
k, order n, is a
geometrical object of which the precise definition will be given in §1. The
geometrical language of the paper proves convenient, but other terminologies are
perhaps more familiar. A finite affine (or Euclidean) plane with n points on each
line is simply a net of
degree n+ 1, order n
(Marshall Hall [1]). A loop of order n is essentially a
net of degree 3, order n (Baer [1], Bates [1]). More
generally, for , a set of k —2
mutually orthogonal n ⨯ n
latin squares may be used to define a net of degree k,
order n (and conversely) by paralleling Bose's
correspondence (Bose [1]) between affine planes and complete sets of orthogonal
latin squares.
Publisher
Canadian Mathematical Society
Cited by
56 articles.
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