MinT - Information on Result #599447

Information on Result #599447

There is no digital (42, 166, 188)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁶⁶, 188, F₄, 124) (dual of [188, 22, 125]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁶⁵, 176, F₄, 124) (dual of [176, 11, 125]-code), but
  - residual code [i] would yield linear OA(4⁴¹, 51, F₄, 31) (dual of [51, 10, 32]-code), but
    - â€œGurâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(4²², 188, S₄, 12), but
  - discarding factors would yield OA(4²², 164, S₄, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 18 187369 733464 > 4²² [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 (42, 167, 188)-net over F₄	[i]	m-Reduction
2	No digital (42, 168, 188)-net over F₄	[i]
3	No digital (42, 169, 188)-net over F₄	[i]