MinT - Information on Result #546794

Information on Result #546794

There is no linear OA(3¹⁹⁷, 280, F₃, 126) (dual of [280, 83, 127]-code), because residual code would yield OA(3⁷¹, 153, S₃, 42), but

the linear programming bound shows that MÂ â‰¥ 1 055633 583684 412124 576484 170255 131218 780961 470521 927693 463389 568320 189199 289559 169330 933131 798207 551957 567481 144539 850575 395329 102764 159939 358868 077128 618402 122131 171260 366925 398215 527745 180439 670326 837896 090390 666310 679248 321377 576820 431328 275321 422069 606660 949118 551478 240579 301418 914961 095796 891840 / 138 376916 366765 245149 784082 130406 254967 569712 303599 812312 770276 538679 404780 518662 697999 679212 679952 906967 837259 967292 004231 340859 946531 558376 639875 802868 726402 799726 504048 508110 636251 941347 913705 438595 007008 728154 695053 276605 319416 010222 452132 016051 115790 666606 828591 > 3⁷¹ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(3¹⁹⁸, 281, F₃, 127) (dual of [281, 83, 128]-code)	[i]	Truncation
2	No linear OA(3¹⁹⁹, 282, F₃, 128) (dual of [282, 83, 129]-code)	[i]	Truncation
3	No linear OOA(3¹⁹⁸, 280, F₃, 2, 127) (dual of [(280, 2), 362, 128]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(3¹⁹⁹, 280, F₃, 2, 128) (dual of [(280, 2), 361, 129]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(3¹⁹⁷, 280, F₃, 2, 126) (dual of [(280, 2), 363, 127]-NRT-code)	[i]	Depth Reduction
6	No linear OOA(3¹⁹⁷, 280, F₃, 3, 126) (dual of [(280, 3), 643, 127]-NRT-code)	[i]
7	No linear OOA(3¹⁹⁷, 280, F₃, 4, 126) (dual of [(280, 4), 923, 127]-NRT-code)	[i]
8	No linear OOA(3¹⁹⁷, 280, F₃, 5, 126) (dual of [(280, 5), 1203, 127]-NRT-code)	[i]
9	No digital (71, 197, 280)-net over F₃	[i]	Extracting Embedded Orthogonal Array