MinT - Information on Result #599416

Information on Result #599416

There is no digital (38, 140, 204)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁴⁰, 204, F₄, 102) (dual of [204, 64, 103]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹³⁹, 163, F₄, 102) (dual of [163, 24, 103]-code), but
  - constructionÂ Y1 [i] would yield
    1. 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(4²⁴, 163, S₄, 14), but
      - discarding factors would yield OA(4²⁴, 134, S₄, 14), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 292 368491 029312 > 4²⁴ [i]
2. OA(4⁶⁴, 204, S₄, 41), but
  - discarding factors would yield OA(4⁶⁴, 203, S₄, 41), but
    - the linear programming bound shows that MÂ â‰¥ 9237 828678 014661 888733 201438 074087 629177 850315 553208 766694 988543 356653 154675 278877 490717 655040 / 25 848321 162508 053807 967718 560003 483887 415061 992757 599441 > 4⁶⁴ [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No digital (38, 141, 204)-net over F₄	[i]		m-Reduction