MinT - Information on Result #599417

Information on Result #599417

There is no digital (38, 142, 199)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁴², 199, F₄, 104) (dual of [199, 57, 105]-code), but

constructionÂ Y1 [i] would yield
1. 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]
2. 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).

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		Method
1	No digital (38, 143, 199)-net over F₄	[i]	m-Reduction
2	No digital (38, 144, 199)-net over F₄	[i]
3	No digital (38, 145, 199)-net over F₄	[i]