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- W4386204087 abstract "Abstract In this paper, we give a geometric construction of the three strong non-lifted $$(3mod 5)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mspace /> <mml:mo>mod</mml:mo> <mml:mspace /> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -arcs in $${{,textrm{PG},}}(3,5)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mrow> <mml:mspace /> <mml:mtext>PG</mml:mtext> <mml:mspace /> </mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> of respective sizes 128, 143, and 168, and construct an infinite family of non-lifted, strong $$(tmod q)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mspace /> <mml:mo>mod</mml:mo> <mml:mspace /> <mml:mi>q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -arcs in $${{,textrm{PG},}}(r,q)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mrow> <mml:mspace /> <mml:mtext>PG</mml:mtext> <mml:mspace /> </mml:mrow> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> with $$t=(q+1)/2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mi>q</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> for all $$rge 3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and all odd prime powers q ." @default.
- W4386204087 created "2023-08-28" @default.
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- W4386204087 date "2023-08-27" @default.
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- W4386204087 title "The geometry of $$(tmod q)$$-arcs" @default.
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- W4386204087 doi "https://doi.org/10.1007/s10623-023-01290-w" @default.
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