MinT - Information on Result #547785

Information on Result #547785

There is no linear OA(3¹³⁶, 198, F₃, 87) (dual of [198, 62, 88]-code), because constructionÂ Y1 would yield

linear OA(3¹³⁵, 164, F₃, 87) (dual of [164, 29, 88]-code), but
- constructionÂ Y1 [i] would yield
  1. OA(3¹³⁴, 150, S₃, 87), but
    - the linear programming bound shows that MÂ â‰¥ 1998 191076 053927 805178 143382 564872 985089 052204 487349 698881 740338 723055 870219 / 227413 116931 > 3¹³⁴ [i]
  2. OA(3²⁹, 164, S₃, 14), but
    - discarding factors would yield OA(3²⁹, 163, S₃, 14), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 69 685080 318363 > 3²⁹ [i]
OA(3⁶², 198, S₃, 34), but
- discarding factors would yield OA(3⁶², 187, S₃, 34), but
  - the linear programming bound shows that MÂ â‰¥ 86 582238 519540 759403 959995 312746 663126 603948 166833 519820 296875 / 223 323463 041708 430754 736757 380607 > 3⁶² [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(3¹³⁷, 199, F₃, 88) (dual of [199, 62, 89]-code)	[i]	Truncation
2	No linear OOA(3¹³⁷, 198, F₃, 2, 88) (dual of [(198, 2), 259, 89]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(3¹³⁶, 198, F₃, 2, 87) (dual of [(198, 2), 260, 88]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(3¹³⁶, 198, F₃, 3, 87) (dual of [(198, 3), 458, 88]-NRT-code)	[i]
5	No linear OOA(3¹³⁶, 198, F₃, 4, 87) (dual of [(198, 4), 656, 88]-NRT-code)	[i]
6	No linear OOA(3¹³⁶, 198, F₃, 5, 87) (dual of [(198, 5), 854, 88]-NRT-code)	[i]
7	No digital (49, 136, 198)-net over F₃	[i]	Extracting Embedded Orthogonal Array