论文信息 - Unitals and replaceable t-nests

Unitals and replaceable t-nests

Let U be a known unital of PG(2, q), q odd, and let N be a t-nest in a regular spread S. Suppose we replace N by a replacement set N to form the new spread S ′ = (S\N)∪ N ). Using the Bruck-Bose correspondence, we look at the affine points of U in P(S) ∼= PG(2, q) and see whether the corresponding affine point set in the new plane P(S ′) can be completed to a unital.

Susan G. Barwick | D. J. Marshall

[1] Gloria Rinaldi. Hyperbolic unitals in the Hall planes , 1995 .

[2] K. Grüning,et al. A class of unitals of order q which can be embedded in two different planes of order q2 , 1987 .

[3] R. C. Bose,et al. Linear representations of projective planes in projective spaces , 1966 .

[4] Susan G. Barwick. A class of Buekenhout unitals in the Hall plane , 1996 .

[5] Susan G. Barwick. Unitals in the Hall plane , 1997 .

[6] Gloria Rinaldi. Construction of unitals in the Hall planes , 1995 .

[7] F. Buekenhout. Existence of unitals in finite translation planes of order q2 with a kernel of order q , 1976 .

[8] Rudolf Metz. On a class of unitals , 1979 .

[9] Susan G. Barwick. A characterization of the classical unital , 1994 .

[10] G. Ebert,et al. A New Class of Translation Planes , 1988 .

[11] Aart Blokhuis,et al. Finite Geometries , 2018, Des. Codes Cryptogr..

[12] S. G. Barwick,et al. Unitals in Projective Planes , 2008 .

[13] Replaceable Nests , 2007 .

[14] Johannes André,et al. Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe , 1954 .

[15] R. Weida. An extension of Bruen chains , 1989 .

[16] R. C. Bose,et al. The construction of translation planes from projective spaces , 1964 .