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MUBS INEQUIVALENCE AND AFFINE PLANES
, 2011
"... There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between com ..."
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There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes “old ” results that do not appear to be wellknown concerning known families of complete sets of MUBs and their associated planes.
Orthogonal Dual Hyperovals, Symplectic Spreads and Orthogonal Spreads
"... Orthogonal spreads in orthogonal spaces of type V + (2n + 2, 2) produce large numbers of rank n dual hyperovals in orthogonal spaces of type V + (2n, 2). The construction resembles the method for obtaining symplectic spreads in V (2n, q) from orthogonal spreads in V + (2n + 2, q) when q is even. ..."
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Orthogonal spreads in orthogonal spaces of type V + (2n + 2, 2) produce large numbers of rank n dual hyperovals in orthogonal spaces of type V + (2n, 2). The construction resembles the method for obtaining symplectic spreads in V (2n, q) from orthogonal spreads in V + (2n + 2, q) when q is even.