MinT - Information on Result #599411

Information on Result #599411

There is no digital (37, 139, 163)-net over F₄, because extracting embedded orthogonal array would yield 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]

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 (37, 140, 163)-net over F₄	[i]		m-Reduction
2	No digital (37, 141, 163)-net over F₄	[i]
3	No digital (37, 142, 163)-net over F₄	[i]
4	No digital (37, 143, 163)-net over F₄	[i]
5	No digital (37, 144, 163)-net over F₄	[i]
6	No digital (37, 145, 163)-net over F₄	[i]
7	No digital (37, 146, 163)-net over F₄	[i]
8	No digital (37, 147, 163)-net over F₄	[i]
9	No digital (37, 148, 163)-net over F₄	[i]