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Anagrafe della Ricerca dell'Università degli Studi di Perugia.
EnglishWe improve the known bounds on r(n):=min{lambda | an (n^2,n,lambda)-RBIBD exists} in the case where n+1 is a prime power. In such a case r(n) is proved to be at most n+1. If, in addition, n+1 is the product of twin prime powers, then r(n)<=n/2. We also improve the known bounds on p(n):=min{lambda | an (n^2+n+1,n+1,lambda)-BIBD exists} in the case where n^2+n+1 is a prime power. In such a case p(n) is bounded at worst by $\lfloor{n+1\over2}\rfloor$ but better bounds could be obtained exploiting the multiplicative structure of GF(n^2+n+1). Finally, we present an unpublished construction by M. Greig giving a quasidouble affine plane of order n for every positive integer n such that n-1 and n+1 are prime powers.
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| Titolo: | Small quasimultiple of affine and projective planes; some improved bounds |
| Autori: | |
| Data di pubblicazione: | 1998 |
| Rivista: | |
| Abstract: | We improve the known bounds on r(n):=min{lambda | an (n^2,n,lambda)-RBIBD exists} in the case where n+1 is a prime power. In such a case r(n) is proved to be at most n+1. If, in addition, n+1 is the product of twin prime powers, then r(n)<=n/2. We also improve the known bounds on p(n):=min{lambda | an (n^2+n+1,n+1,lambda)-BIBD exists} in the case where n^2+n+1 is a prime power. In such a case p(n) is bounded at worst by $\lfloor{n+1\over2}\rfloor$ but better bounds could be obtained exploiting the multiplicative structure of GF(n^2+n+1). Finally, we present an unpublished construction by M. Greig giving a quasidouble affine plane of order n for every positive integer n such that n-1 and n+1 are prime powers. |
| Handle: | http://hdl.handle.net/11391/920464 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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