2009
DOI: 10.1007/s00022-009-0009-3
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On sizes of complete caps in projective spaces PG(n, q) and arcs in planes PG(2, q)

Abstract: More than thirty new upper bounds on the smallest size t2(2, q) of a complete arc in the plane PG(2, q) are obtained for 169 ≤ q ≤ 839. New upper bounds on the smallest size t2(n, q) of the complete cap in the space PG(n, q) are given for n = 3 and 25 ≤ q ≤ 97, q odd; n = 4 and q = 7, 8, 11, 13, 17; n = 5 and q = 5, 7, 8, 9; n = 6 and q = 4, 8. The bounds are obtained by computer search for new small complete arcs and caps. New upper bounds on the largest size m2(n, q) of a complete cap in PG(n, q) are given f… Show more

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Cited by 37 publications
(81 citation statements)
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References 48 publications
(175 reference statements)
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“…It should be noticed however that some of the entries in the Tables in [8,7] arose as particular cases of the above-mentioned incorrect results. Actually, all these entries are correct since they also appear in the tables performed in [6] using MAGMA package. Our computer-aided search confirms the validity of those entries at least for q ≤ 125.…”
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confidence: 94%
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“…It should be noticed however that some of the entries in the Tables in [8,7] arose as particular cases of the above-mentioned incorrect results. Actually, all these entries are correct since they also appear in the tables performed in [6] using MAGMA package. Our computer-aided search confirms the validity of those entries at least for q ≤ 125.…”
mentioning
confidence: 94%
“…In Section 7, we report on the known results obtained by computer-aided search in PG(2, q) for complete ( 1 2 (q +3)+n)-arcs with n ≥ 3 in PG(2, q) sharing exactly 1 2 (q +3) points with a conic. In [6], the authors obtained a complete classification for q ≤ 29 using a different approach. Interestingly, they found a new example for q = 27.…”
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confidence: 99%
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“…Problems connected with small complete arcs in PG (2, q) are considered in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]20,[23][24][25][26][27][28][30][31][32][33][34][35][36][37][38][39][40][41][42][44][45][46][47][48]50,51,[54][55][56][57][58][61][62][63]…”
Section: Introduction the Main Resultsmentioning
confidence: 99%
“…[4], see also [10,12,24,26,30] and references therein. For q = 2 16 , 2 17 complete arcs are obtained in [6].…”
Section: Introduction the Main Resultsmentioning
confidence: 99%