MinT - Information on Result #547878

Information on Result #547878

There is no linear OA(4¹⁴², 199, F₄, 104) (dual of [199, 57, 105]-code), because constructionÂ Y1 would yield

linear OA(4¹⁴¹, 163, F₄, 104) (dual of [163, 22, 105]-code), but
- constructionÂ Y1 [i] would yield
  1. OA(4¹⁴⁰, 151, S₄, 104), but
    - 2 times truncation [i] would yield OA(4¹³⁸, 149, S₄, 102), but
      - the linear programming bound shows that MÂ â‰¥ 11 769278 720446 703333 267659 747956 551886 187319 922656 933070 157940 129170 842786 675855 465333 653504 / 85 907459 > 4¹³⁸ [i]
  2. OA(4²², 163, S₄, 12), but
    - the linear programming bound shows that MÂ â‰¥ 22822 886502 605724 057600 / 1273 153051 > 4²² [i]
OA(4⁵⁷, 199, S₄, 36), but
- discarding factors would yield OA(4⁵⁷, 195, S₄, 36), but
  - the linear programming bound shows that MÂ â‰¥ 494 490067 436667 455875 598203 818411 591542 653847 684514 372082 636620 702806 966272 / 22309 972171 916724 959618 830756 395146 773299 > 4⁵⁷ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4¹⁴³, 200, F₄, 105) (dual of [200, 57, 106]-code)	[i]	Truncation
2	No linear OA(4¹⁴⁴, 201, F₄, 106) (dual of [201, 57, 107]-code)	[i]
3	No linear OA(4¹⁴⁵, 202, F₄, 107) (dual of [202, 57, 108]-code)	[i]
4	No linear OOA(4¹⁴³, 199, F₄, 2, 105) (dual of [(199, 2), 255, 106]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4¹⁴⁴, 199, F₄, 2, 106) (dual of [(199, 2), 254, 107]-NRT-code)	[i]
6	No linear OOA(4¹⁴⁵, 199, F₄, 2, 107) (dual of [(199, 2), 253, 108]-NRT-code)	[i]
7	No linear OOA(4¹⁴², 199, F₄, 2, 104) (dual of [(199, 2), 256, 105]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4¹⁴², 199, F₄, 3, 104) (dual of [(199, 3), 455, 105]-NRT-code)	[i]	Depth Reduction
9	No digital (38, 142, 199)-net over F₄	[i]	Extracting Embedded Orthogonal Array